1.
The graph shows the variation with time t of the velocity v of an object.
v
t
Which one of the following graphs best represents the variation with time t of the acceleration a
of the object?
A.
a
0
C.
B.
0
0
0
t
a
D.
0
t
a
0
t
0
t
a
0
(1)
2.
A ball, initially at rest, takes time t to fall through a vertical distance h. If air resistance is
ignored, the time taken for the ball to fall from rest through a vertical distance 9h is
A.
3t.
B.
5t.
C.
9t.
D.
10t.
(1)
1
3.
A raindrop falling through air reaches a terminal velocity before hitting the ground. At terminal
velocity, the frictional force on the raindrop is
A.
zero.
B.
less than the weight of the raindrop.
C.
greater than the weight of the raindrop.
D.
equal to the weight of the raindrop.
(1)
4.
The diagram below shows the path of a projectile in the absence of air resistance.
Vertical
position
Horizontal position
Which one of the following diagrams best represents the path of the projectile under the same
initial conditions when the air resistance is taken into account? (The path in absence of air
resistance is shown for comparison as a dotted line.)
A.
B.
Vertical
position
Vertical
position
Horizontal position
C.
Horizontal position
D.
Vertical
position
Horizontal position
Vertical
position
Horizontal position
(1)
2
5.
A sailing boat is moving with constant velocity v to the right parallel to the dock.
Sailor Hulot, up on the mast, drops his telescope at the moment he is opposite Lucie who is
standing on the dock. Which one of the following best shows the path of the falling telescope as
seen by Lucie?
A.
B.
C.
D.
(1)
6.
This question is about forces on charged particles.
(a)
A charged particle is situated in a field of force. Deduce the nature of the force-field
(magnetic, electric or gravitational) when the force on the particle
(i)
is along the direction of the field regardless of its charge and velocity;
...........................................................................................................................
(ii)
is independent of the velocity of the particle but depends on its charge;
...........................................................................................................................
3
(iii)
depends on the velocity of the particle and its charge.
...........................................................................................................................
(5)
(b)
An electron is accelerated from rest in a vacuum through a potential difference of 2.1 kV.
Deduce that the final speed of the electron is 2.7 × 107 m s–1.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
The electron in (b) then enters a region of uniform electric field between two conducting
horizontal metal plates as shown below.
+95 V
Path of
electron
P
2.2 cm
7
2.7 × 10 m s
–1
0V
12 cm
The electric field outside the region of the plates may be assumed to be zero. The potential
difference between the plates is 95 V and their separation is 2.2 cm.
As the electron enters the region of the electric field, it is travelling parallel to the plates.
(c)
(i)
On the diagram above, draw an arrow at P to show the direction of the force due to
the electric field acting on the electron.
(1)
4
(ii)
Calculate the force on the electron due to the electric field.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(d)
The plates in the diagram above are of length 12 cm. Determine
(i)
the time of flight between the plates.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(1)
(ii)
the vertical distance moved by the electron during its passage between the plates.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(e)
Suggest why gravitational effects were not considered when calculating the deflection of
the electron.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
5
(f)
In a mass spectrometer, electric and magnetic fields are used to select charged particles of
one particular speed. A uniform magnetic field is applied in the region between the plates,
such that the electron passes between the plates without being deviated.
For this magnetic field,
(i)
state and explain its direction;
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(ii)
determine its magnitude.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(g)
The electric and magnetic fields in (f) remain unchanged. Giving a brief explanation in
each case, compare qualitatively the deflection of the electron in (f) with that of
(i)
an electron travelling at a greater initial speed;
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(ii)
a proton having the same speed;
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
6
(iii)
an alpha particle (α-particle) having the same speed.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(7)
(Total 30 marks)
7.
An athlete runs round a circular track at constant speed. Which one of the following graphs best
represents the variation with time t of the magnitude d of the displacement of the athlete from
the starting position during one lap of the track?
A. d
0
B. d
0
t
C. d
0
0
0
t
0
t
D. d
0
t
0
(1)
7
8.
A ball is released from rest near the surface of the Moon. Which one of the following quantities
increases at a constant rate?
A.
Only distance fallen
B.
Only speed
C.
Only speed and distance fallen
D.
Only speed and acceleration
(1)
9.
A stone is thrown horizontally from the top of a high cliff. Assuming air resistance is negligible,
what is the effect of gravitational force on the horizontal and on the vertical components of the
velocity of the stone?
Vertical component of velocity
Horizontal component of velocity
A.
increases to a constant value
stays constant
B.
increases continuously
stays constant
C.
increases to a constant value
decreases to zero
D.
increases continuously
decreases to zero
(1)
10.
This question is about the kinematics of an elevator (lift).
(a)
Explain the difference between the gravitational mass and the inertial mass of an object.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
8
An elevator (lift) starts from rest on the ground floor and comes to rest at a higher floor. Its
motion is controlled by an electric motor. A simplified graph of the variation of the elevator’s
velocity with time is shown below.
velocity / m s –1
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0 12.0
time / s
(b)
The mass of the elevator is 250 kg. Use this information to calculate
(i)
the acceleration of the elevator during the first 0.50 s.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(ii)
the total distance travelled by the elevator.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
9
(iii)
the minimum work required to raise the elevator to the higher floor.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(iv)
the minimum average power required to raise the elevator to the higher floor.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(v)
the efficiency of the electric motor that lifts the elevator, given that the input power
to the motor is 5.0 kW.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(c)
On the graph axes below, sketch a realistic variation of velocity for the elevator. Explain
your reasoning. (The simplified version is shown as a dotted line)
velocity / m s –1
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0 12.0
time / s
(2)
10
The elevator is supported by a cable. The diagram below is a free-body force diagram for when
the elevator is moving upwards during the first 0.50 s.
tension
weight
(d)
In the space below, draw free-body force diagrams for the elevator during the following
time intervals.
(i)
0.5 to 11.50 s
(ii)
11.50 to 12.00 s
(3)
A person is standing on weighing scales in the elevator. Before the elevator rises, the reading on
the scales is W.
11
(e)
On the axes below, sketch a graph to show how the reading on the scales varies during
the whole 12.00 s upward journey of the elevator. (Note that this is a sketch graph – you
do not need to add any values.)
reading on scales
W
0.00
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0 12.0
time / s
(3)
(f)
The elevator now returns to the ground floor where it comes to rest. Describe and explain
the energy changes that take place during the whole up and down journey.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(4)
(Total 25 marks)
12
11.
This question is about projectile motion and the use of an energy argument to find the speed
with which a thrown stone lands in the sea.
Christina stands close to the edge of a vertical cliff and throws a stone. The diagram below (not
drawn to scale) shows part of the trajectory of the stone. Air resistance is negligible.
P
15 m s –1
O
Q
25 m
sea
Point P on the diagram is the highest point reached by the stone and point Q is at the same
height above sea level as point O.
(a)
At point P on the diagram above draw arrows to represent
(i)
the acceleration of the stone (label this A).
(1)
(ii)
the velocity of the stone (label this V).
(1)
The stone leaves Christina’s hand (point O) at a speed of 15 m s−1 in the direction shown. Her
hand is at a height of 25 m above sea level. The mass of the stone is 160 g. The acceleration due
to gravity g = 10 m s−2.
13
(b)
(i)
Calculate the kinetic energy of the stone immediately after it leaves Christina’s
hand.
...........................................................................................................................
...........................................................................................................................
(1)
(ii)
State the value of the kinetic energy at point Q.
...........................................................................................................................
(1)
(iii)
Calculate the loss in potential energy of the stone in falling from point Q to hitting
the sea.
...........................................................................................................................
...........................................................................................................................
(1)
(iv)
Determine the speed with which the stone hits the sea.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(Total 7 marks)
12.
A car is heading due East at a speed of 10 m s−1. A bird is flying due North at a speed of
4 m s−1, as shown below.
N
W
4ms
E
–1
S
Car
10 m s –1
Bird
Which one of the following vectors represents the velocity of the bird relative to a person in the
car?
14
A.
B.
C.
D.
(1)
13.
A stone is thrown from O at an angle to the horizontal. Which sketch below best shows the path
of the stone when air resistance is not neglected? On each sketch, the broken line shows the
path for the same stone in a vacuum.
A.
B.
O
C.
O
D.
O
O
(1)
15
14.
Peter and Susan both stand on the edge of a vertical cliff.
V (Peter)
V (Susan)
Sea
Susan throws a stone vertically downwards and, at the same time, Peter throws a stone vertically
upwards. The speed V with which both stones are thrown is the same. Neglecting air resistance,
which one of the following statements is true?
A.
The stone thrown by Susan will hit the sea with a greater speed than the stone thrown by
Peter.
B.
Both stones will hit the sea with the same speed no matter what the height of the cliff.
C.
In order to determine which stone hits the sea first, the height of the cliff must be known.
D.
In order to determine which stone hits the sea first both the height of the cliff and the
mass of each stone must be known.
(1)
16
15.
A ball is dropped from rest at time t = 0 on to a horizontal surface from which it rebounds. The
graph shows the variation of time t with speed v of the ball.
v
A
C
0
0
B
D
t
Which one of the following best represents the point at which the ball just loses contact with the
surface after the first bounce?
A.
A
B.
B
C.
C
D.
D
(1)
17
16.
Juan is standing on the platform at a railway station. A train passes through the station with
speed 20 m s–1 in the direction shown measured relative to the platform. Carmen is walking
along one of the carriages of the train with a speed of 2.0 m s–1 measured relative to the carriage
in the direction shown. Velocity is measured as positive in the direction shown on the diagram.
Carmen
2.0 ms –1
20 ms –1
Juan
platform
velocity measured as a
positive in this direction
The velocity of Carmen relative to Juan is
A.
–22 m s–1.
B.
–18 m s–1.
C.
+18 m s–1.
D.
+22 m s–1.
(1)
17.
This question is about waves and wave motion.
(a)
(i)
Define what is meant by the speed of a wave.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
18
(ii)
Light is emitted from a candle flame. Explain why, in this situation, it is correct to
refer to the “speed of the emitted light”, rather than its velocity.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(b)
(i)
Define, by reference to wave motion, what is meant by displacement.
...........................................................................................................................
...........................................................................................................................
(2)
(ii)
By reference to displacement, describe the difference between a longitudinal wave
and a transverse wave.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
The centre of an earthquake produces both longitudinal waves (P waves) and transverse waves
(S waves). The graph below shows the variation with time t of the distance d moved by the two
types of wave.
d / km
S wave
P wave
1200
800
400
0
0
25
50
75
100
125
150
175
200
225
t/s
19
(c)
Use the graph to determine the speed of
(i)
the P waves.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(1)
(ii)
the S waves.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(1)
The waves from an earthquake close to the Earth’s surface are detected at three laboratories L1,
L2 and L3. The laboratories are at the corners of a triangle so that each is separated from the
others by a distance of 900 km, as shown in the diagram below.
900 km
L1
L2
L3
20
The records of the variation with time of the vibrations produced by the earthquake as detected
at the three laboratories are shown below. All three records were started at the same time.
L1
L2
start of trace
L3
time
On each record, one pulse is made by the S wave and the other by the P wave. The separation of
the two pulses is referred to as the S-P interval.
(d)
(i)
On the trace produced by laboratory L2, identify, by reference to your answers in
(c), the pulse due to the P wave (label the pulse P).
(1)
(ii)
Using evidence from the records of the earthquake, state which laboratory was
closest to the site of the earthquake.
...........................................................................................................................
(1)
(iii)
State three separate pieces of evidence for your statement in (d)(ii).
(3)
1.
.................................................................................................................
.................................................................................................................
2.
.................................................................................................................
.................................................................................................................
3.
.................................................................................................................
.................................................................................................................
21
(iv)
The S-P intervals are 68 s, 42 s and 27 s for laboratories L1, L2 and L3 respectively.
Use the graph, or otherwise, to determine the distance of the earthquake from each
laboratory. Explain your working.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
Distance from L1 = ......................km
...........................................................................................................................
Distance from L2 = ......................km
...........................................................................................................................
Distance from L3 = ......................km
...........................................................................................................................
(4)
(v)
Mark on the diagram a possible site of the earthquake.
(1)
There is a tall building near to the site of the earthquake, as illustrated below.
building
ground
direction of vibrations
The base of the building vibrates horizontally due to the earthquake.
22
(e)
(i)
On the diagram above, draw the fundamental mode of vibration of the building
caused by these vibrations.
(1)
The building is of height 280 m and the mean speed of waves in the structure of the building is
3.4 × 103 ms–1.
(ii)
Explain quantitatively why earthquake waves of frequency about 6 Hz are likely to
be very destructive.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(Total 25 marks)
23
18.
A ball is dropped from rest at time t = 0 on to a horizontal surface from which it rebounds.
Which one of the following graphs best shows the variation of speed v of the ball with time t
from the time t = 0 to the time that the ball leaves the surface?
A.
B.
v
0
C.
v
0
D.
v
0
0
t
0
t
0
t
0
t
v
0
(1)
19.
Which one of the following is a true statement concerning the vertical component of the
velocity and the acceleration of a projectile when it is at its maximum height? (The acceleration
of free fall is g.)
Vertical component of velocity
Acceleration
A.
maximum
zero
B.
maximum
g
C.
zero
zero
D.
zero
g
(1)
24
20.
This question is about earthquake waves.
(a)
(i)
Light is emitted from a candle flame. Explain why, in this situation, it is correct to
refer to the “speed of the emitted light”, rather than its velocity.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(ii)
By reference to displacement, describe the difference between a longitudinal wave
and a transverse wave.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
The centre of an earthquake produces both longitudinal waves (P waves) and transverse waves
(S waves). The graph below shows the variation with time t of the distance d moved by the two
types of wave.
d / km
S wave
P wave
1200
800
400
0
0
25
50
75
100
125
150
175
200
225
t/s
25
(b)
Use the graph to determine the speed of
(i)
the P waves.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(1)
(ii)
the S waves.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(1)
The waves from an earthquake close to the Earth’s surface are detected at three laboratories L1,
L2 and L3. The laboratories are at the corners of a triangle so that each is separated from the
others by a distance of 900 km, as shown in the diagram below.
900 km
L1
L2
L3
26
The records of the variation with time of the vibrations produced by the earthquake as detected
at the three laboratories are shown below. All three records were started at the same time.
L1
L2
start of trace
L3
time
On each record, one pulse is made by the S wave and the other by the P wave. The separation of
the two pulses is referred to as the S-P interval.
(c)
(i)
On the trace produced by laboratory L2, identify, by reference to your answers in
(b), the pulse due to the P wave (label the pulse P).
(1)
(ii)
Using evidence from the records of the earthquake, state which laboratory was
closest to the site of the earthquake.
...........................................................................................................................
(1)
(iii)
State three separate pieces of evidence for your statement in (c)(ii).
1
.................................................................................................................
.................................................................................................................
2
.................................................................................................................
.................................................................................................................
3
.................................................................................................................
.................................................................................................................
(3)
27
(iv)
The S-P intervals are 68 s, 42 s and 27 s for laboratories L1, L2 and L3 respectively.
Use the graph, or otherwise, to determine the distance of the earthquake from each
laboratory. Explain your working.
Distance from L1 = ......................km
...........................................................................................................................
Distance from L2 = ......................km
...........................................................................................................................
Distance from L3 = ......................km
...........................................................................................................................
(4)
(v)
Mark on the diagram a possible site of the earthquake.
(1)
There is a tall building near to the site of the earthquake, as illustrated below.
building
ground
direction of vibrations
The base of the building vibrates horizontally due to the earthquake.
(d)
(i)
On the diagram, draw the fundamental mode of vibration of the building caused by
these vibrations.
(1)
28
The building is of height 280 m and the mean speed of waves in the structure of the building is
3.4 × 103 ms–1.
(ii)
Explain quantitatively why earthquake waves of frequency about 6 Hz are likely to
be very destructive.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(Total 21 marks)
21.
The diagram below shows the variation with time t of the velocity v of an object.
v
0
0
t
The area between the line of the graph and the time-axis represents
A.
the average velocity of the object.
B.
the displacement of the object.
C.
the impulse acting on the object.
D.
the work done on the object.
(1)
29
22.
The diagram below shows the variation with time t of the velocity v of an object.
v
0
t
0
Which one of the following graphs shows the variation with time t of the acceleration a of the
object?
A.
B.
a
0
0
0
C.
a
t
D.
a
t
0
a
0
0
t
0
0
t
(1)
30
23.
This question is about projectile motion.
A small steel ball is projected horizontally from the edge of a bench. Flash photographs of the
ball are taken at 0.10 s intervals. The resulting images are shown against a scale as in the
diagram below.
0
20
distance / cm
40
60
80
100
0
20
40
60
distance / cm
80
100
120
140
(a)
Use the diagram to determine
(i)
the constant horizontal speed of the ball.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
31
(ii)
the acceleration of free fall.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(b)
Mark on the diagram the position of the ball 0.50 s after projection.
In the space below, you should carry out any calculations so that you can accurately
position the ball.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(c)
A second ball is projected from the bench at the same speed as the original ball. The ball
has small mass so that air resistance cannot be neglected. Draw on the diagram the
approximate shape of the path you would expect the ball to take.
(3)
(Total 10 marks)
24.
A stone X is thrown vertically upwards with speed v from the top of a building. At the same
time, a second stone Y is thrown vertically downwards with the same speed v as shown.
v
X
Y
v
Building
32
Air resistance is negligible. Which one of the following statements is true about the speeds with
which the stones hit the ground at the base of the building?
A.
The speed of stone X is greater than that of stone Y.
B.
The speed of stone Y is greater than that of stone X.
C.
The speed of stone X is equal to that of stone Y.
D.
Any statement about the speeds depends on the height of the building.
(1)
25.
The graph below shows the variation with time of the distance moved by a car along a straight
road. During which time interval does the car have its greatest acceleration?
distance
moved
time
A
B
C
D
(1)
33
26.
This question is about throwing a stone from a cliff.
Antonia stands at the edge of a vertical cliff and throws a stone vertically upwards.
v = 8.0ms –1
Sea
The stone leaves Antonia’s hand with a speed v = 8.0ms–1.
The acceleration of free fall g is 10 m s–2 and all distance measurements are taken from the
point where the stone leaves Antonia’s hand.
(a)
Ignoring air resistance calculate
(i)
the maximum height reached by the stone.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(ii)
the time taken by the stone to reach its maximum height.
...........................................................................................................................
...........................................................................................................................
(1)
34
The time between the stone leaving Antonia’s hand and hitting the sea is 3.0 s.
(b)
Determine the height of the cliff.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(Total 6 marks)
27.
The minute hand of a clock hung on a vertical wall has length L.
P
L
The minute hand is observed at the time shown above and then again, 30 minutes later.
What is the displacement of, and the distance moved by, the end P of the minute hand during
this time interval?
displacement
distance moved
A.
2L vertically downwards
πL
B.
2L vertically upwards
πL
C.
2L vertically downwards
2L
D.
2L vertically upwards
2L
(1)
35
28.
A ball is thrown horizontally from the top of a cliff. Air resistance is negligible. Which of the
following diagrams best represents the subsequent path of the ball?
A.
B.
C.
D.
(1)
29.
This question is about trajectory motion.
Antonia stands at the edge of a vertical cliff and throws a stone upwards at an angle of 60° to
the horizontal.
v = 8.0ms –1
60°
Sea
36
The stone leaves Antonia’s hand with a speed v = 8.0 m s–1. The time between the stone leaving
Antonia’s hand and hitting the sea is 3.0 s.
The acceleration of free fall g is 10 m s–2 and all distance measurements are taken from the
point where the stone leaves Antonia’s hand.
Ignoring air resistance calculate
(a)
the maximum height reached by the stone.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(b)
the horizontal distance travelled by the stone.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(Total 5 marks)
30.
Which one of the following is a correct definition of displacement?
A.
Distance from a fixed point
B.
Distance moved from a fixed point
C.
Distance from a fixed point in a given direction
D.
Distance moved in a given direction
(1)
37
31.
The variation with time t of the speed v of a car moving along a straight road is shown below.
v
S1
S2
S3
0
0
t
Which area, S1, S2 or S3, or combination of areas, represents the total distance moved by the car
during the time that its speed is reducing?
A.
S1
B.
S3
C.
S1 + S3
D.
S1 + S2 + S3
(1)
32.
This question is about momentum and the kinematics of a proposed journey to Jupiter.
(a)
State the law of conservation of momentum.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
A solar propulsion engine uses solar power to ionize atoms of xenon and to accelerate them. As
a result of the acceleration process, the ions are ejected from the spaceship with a speed of
3.0 × 104 m s–1.
xenon ions
speed = 3.0×104 m s –1
spaceship
mass = 5.4×102 kg
38
(b)
The mass (nucleon) number of the xenon used is 131. Deduce that the mass of one ion of
xenon is 2.2 × 10–25 kg.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(c)
The original mass of the fuel is 81 kg. Deduce that, if the engine ejects 77 × 1018 xenon
ions every second, the fuel will last for 1.5 years. (1 year = 3.2 × 107 s)
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(d)
The mass of the spaceship is 5.4 × 102 kg. Deduce that the initial acceleration of the
spaceship is 8.2 × 10–5 m s–2.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(5)
39
The graph below shows the variation with time t of the acceleration a of the spaceship. The
solar propulsion engine is switched on at time t = 0 when the speed of the spaceship is 1.2 × 103
m s–1.
10.0
9.5
a / ×10– 5m s– 2
9.0
8.5
8.0
0.0
(e)
1.0
2.0
3.0
t / ×107 s
4.0
5.0
6.0
Explain why the acceleration of the spaceship is increasing with time.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(f)
Using data from the graph, calculate the speed of the spaceship at the time when the
xenon fuel has all been used.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(4)
40
(g)
The distance of the spaceship from Earth when the solar propulsion engine is switched on
is very small compared to the distance from Earth to Jupiter. The fuel runs out when the
spaceship is a distance of 4.7 × 10–11 m from Jupiter. Estimate the total time that it would
take the spaceship to travel from Earth to Jupiter.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(Total 19 marks)
33.
A ball is held at rest in air. The ball is then released. Which one of the following graphs best
shows the variation with time t of the distance d fallen by the ball?
A. d
0
B. d
0
0
t
C. d
0
0
t
0
t
D. d
0
0
t
(1)
41
34.
A boy throws a small stone at an angle to the horizontal.
Which one of the following sketches best shows the path of the stone as it rises and then falls
back to Earth? Air resistance is negligible and the acceleration of free fall is constant.
A.
B.
C.
D.
(1)
35.
This question is about projectile motion.
A marble is projected horizontally from the edge of a wall 1.8 m high with an initial speed V.
V
1.8 m
ground
42
A series of flash photographs are taken of the marble. The photographs are combined into a
single photograph as shown below. The images of the marble are superimposed on a grid that
shows the horizontal distance x and vertical distance y travelled by the marble.
The time interval between each image of the marble is 0.10 s.
0
0.50
x/m
1.0
1.5
2.0
0
–0.50
y/m
–1.0
–1.5
–2.0
(a)
On the images of the marble at x = 0.50 m and x = 1.0 m, draw arrows to represent the
horizontal velocity VH and vertical velocity VV.
(2)
(b)
On the photograph, draw a suitable line to determine the horizontal distance d from the
base of the wall to the point where the marble hits the ground. Explain your reasoning.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
43
(c)
Use data from the photograph to calculate a value of the acceleration of free fall.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(Total 8 marks)
44
36.
A car accelerates uniformly from rest. It then continues at constant speed before the brakes are
applied, bringing the car to rest.
Which of the following graphs best shows the variation with time t of the acceleration a of the
car?
A.
a
0
B.
0
t
0
t
0
t
a
0
D.
t
a
0
C.
0
a
0
(1)
45
37.
Four cars W, X, Y and Z are on a straight road. The graph below shows the variation with time t
of the distance s of each car from a fixed point.
s
X
W
Y
Z
0
0
t
Which car has the greatest speed?
A.
W
B.
X
C.
Y
D.
Z
(1)
38.
A stone is thrown at an angle to the horizontal. Ignoring air resistance, the horizontal component
of the initial velocity of the stone determines the value of
A.
range only.
B.
maximum height only.
C.
range and maximum height.
D.
range and time of flight.
(1)
46
39.
This question is about linear motion.
A police car P is stationary by the side of a road. A car S, exceeding the speed limit, passes the
police car P at a constant speed of 18 m s–1. The police car P sets off to catch car S just as car S
passes the police car P. Car P accelerates at 4.5 m s–2 for a time of 6.0 s and then continues at
constant speed. Car P takes a time t seconds to draw level with car S.
(a)
(i)
State an expression, in terms of t, for the distance car S travels in t seconds.
...........................................................................................................................
(1)
(ii)
Calculate the distance travelled by the police car P during the first 6.0 seconds of
its motion.
...........................................................................................................................
...........................................................................................................................
(1)
(iii)
Calculate the speed of the police car P after it has completed its acceleration.
...........................................................................................................................
...........................................................................................................................
(1)
(iv)
State an expression, in terms of t, for the distance travelled by the police car P
during the time that it is travelling at constant speed.
...........................................................................................................................
(1)
(b)
Using your answers to (a), determine the total time t taken for the police car P to draw
level with car S.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(Total 6 marks)
47
40.
The graph below shows the variation with time t of the acceleration a of a spaceship.
a
0
0
T
t
The spaceship is at rest at t = 0.
The shaded area represents
A.
the distance travelled by the spaceship between t = 0 and t = T.
B.
the speed of the spaceship at t = T.
C.
the rate at which the speed of the spaceship changes between t = 0 and t = T.
D.
the rate at which the acceleration changes between t = 0 and t = T.
(1)
41.
A particle moves from a point P to a point Q in a time T. Which one of the following correctly
defines both the average velocity and average acceleration of the particle?
Average velocity
Average acceleration
A.
displaceme nt of Q and P
T
change in speed from Q to P
T
B.
displaceme nt of Q and P
T
change in velocit y from Q to P
T
C.
distance between Q and P
T
change in speed from Q to P
T
D.
distance between Q and P
T
change in velocit y from Q to P
T
(1)
42.
Two stones, X and Y, of different mass are dropped from the top of a cliff. Stone Y is dropped a
48
short time after stone X. Air resistance is negligible.
Whilst the stones are falling, the distance between them will
A.
decrease if the mass of Y is greater than the mass of X.
B.
increase if the mass of X is greater than the mass of Y.
C.
decrease whether the mass of X is greater or less than the mass of Y.
D.
increase whether the mass of X is greater or less than the mass of Y.
(1)
43.
Kinematics
(a)
State the principle of conservation of energy.
...................................................................................................................................
...................................................................................................................................
(1)
(b)
An aircraft accelerates from rest along a horizontal straight runway and then takes-off.
Discuss how the principle of conservation of energy applies to the energy changes that
take place while the aircraft is accelerating along the runway.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(3)
49
(c)
The mass of the aircraft is 8.0  103 kg.
(i)
The average resultant force on the aircraft while travelling along the runway is 70
kN. The speed of the aircraft just as it lifts off is 75 m s–1. Estimate the distance
travelled along the runway.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(3)
(ii)
The aircraft climbs to a height of 1250 m. Calculate the potential energy gained
during the climb.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(1)
50
When approaching its destination, the pilot puts the aircraft into a holding pattern. This means
the aircraft flies at a constant speed of 90 m s–1 in a horizontal circle of radius 500 m as shown
in the diagram below.
500 m
(d)
For the aircraft in the holding pattern,
(i)
calculate the magnitude of the resultant force on the aircraft;
.........................................................................................................................
.........................................................................................................................
(2)
(ii)
state the direction of the resultant force.
.........................................................................................................................
.........................................................................................................................
(1)
(Total 11 marks)
51
44.
This question is about projectile motion.
A stone is thrown horizontally from the top of a vertical cliff of height 33 m as shown below.
18 m s –1
33 m
sea level
The initial horizontal velocity of the stone is 18 m s–1 and air resistance may be assumed to be
negligible.
(a)
State values for the horizontal and for the vertical acceleration of the stone.
Horizontal acceleration: ............................................................................................
Vertical acceleration: ................................................................................................
(2)
(b)
Determine the time taken for the stone to reach sea level.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(2)
(c)
Calculate the distance of the stone from the base of the cliff when it reaches sea level.
...................................................................................................................................
...................................................................................................................................
(1)
(Total 5 marks)
52
45.
The graph below shows the variation with time t of the acceleration a of a spaceship.
a
0
0
T
t
The spaceship is at rest at t = 0.
The shaded area represents
A.
the distance travelled by the spaceship between t = 0 and t = T.
B.
the speed of the spaceship at t = T.
C.
the rate at which the speed of the spaceship changes between t = 0 and t = T.
D.
the rate at which the acceleration changes between t = 0 and t = T.
(1)
46.
A stone is projected horizontally from the top of a cliff. Neglecting air resistance, which one of
the following correctly describes what happens to the horizontal component of velocity and to
the vertical component of velocity?
Horizontal component of velocity
Vertical component of velocity
A.
Decreases
Increases
B.
Decreases
Constant
C.
Constant
Constant
D.
Constant
Increases
(1)
53
47.
A boat is moving in the direction shown with a speed of 5 m s−1 as measured by Nico who is at
rest on the beach. Aziz walks along the deck of the boat in the direction shown with a speed of 2
m s−1 measured relative to the boat.
positive direction
Aziz
5 m s–1
Nico
If velocity is measured as positive in the direction shown, the velocity of Nico relative to Aziz
is
A.
− 7 m s−1.
B.
− 3 m s−1.
C.
+ 3 m s−1.
D.
+ 7 m s−1.
(1)
48.
The graph below shows the variation with time t of the displacement s of a car. In which time
interval is the speed greatest?
s
0
0 A
B
C
D
t
(1)
54
49.
Two points P and Q are at distances r and 2r respectively from the centre of a compact disc
(CD) as shown.
r
P
2r
Q
When the disc is rotating about its centre, the ratio of the
A.
1
.
2
B.
1.
2.
C.
D.
accelerati on at P
is
accelerati on at Q
2.
(1)
55
50.
This question is about circular motion.
A geo-stationary satellite is one that orbits the Earth in an equatorial plane in the same direction
of rotation as that of the Earth and with an orbital period of 24 hours. Since the period of
rotation of the Earth is 24 hours, this means that the satellite is stationary relative to a point on
the Equator.
(a)
The diagram below shows a geostationary satellite in orbit about the Earth.
not to scale
satellite
Earth
On the diagram above, draw an arrow to show the direction of acceleration of the
satellite.
(1)
(b)
State the name of the force causing the satellite’s acceleration.
...................................................................................................................................
(1)
(c)
The distance of the satellite from the centre of the Earth is 4.2  107 m. Calculate the
acceleration of the satellite.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(3)
(Total 5 marks)
56
51.
This question is about projectile motion.
A stone of mass 0.44 kg is thrown horizontally from the top of a cliff with a speed of 22 m s–1
as shown below.
22 m s–1
32 m
cliff
sea level
The cliff is 32 m high.
(a)
Calculate the total kinetic energy of the stone at sea level assuming air resistance is
negligible.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(3)
(b)
In practice, air resistance is not negligible. During the motion of the stone from the top of
the cliff to sea level, 34 of the total energy of the stone is transferred due to air
resistance. Determine the speed at which the stone reaches sea level.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(2)
(Total 5 marks)
57
52.
An archer shoots an arrow at an angle to the horizontal. Air resistance is negligible. Which of
the following graphs best represents the variation with time of the horizontal component of the
arrow’s velocity from the time it is launched to the time just before it hits the ground?
A.
velocity
B.
velocity
0 0
0
C.
0
time
velocity
D.
0
0
time
time
velocity
0
0
time
(1)
58
53.
A ball is thrown vertically upwards from the ground. The graph shows the variation with time t
of the vertical displacement d of the ball.
d
D
0
0
T
t
Which one of the following gives the final displacement after time T and the average speed
between time t = 0 and time t = T?
Displacement
Average speed
A.
0
0
B.
0
2D
T
C.
2D
2D
T
D.
2D
0
(1)
59
54.
Points P and Q are at distances R and 2R respectively from the centre X of a disc, as shown
below.
Q
P
2R
R
X
The disc is rotating about an axis through X, normal to the plane of the disc. Point P has linear
speed v and centripetal acceleration a. Which one of the following is correct for point Q?
Linear speed
Centripetal acceleration
A.
v
a
B.
v
2a
C.
2v
2a
D.
2v
4a
(1)
60
55.
This question is about the trajectory of a golf ball.
A golfer hits a golf ball at point A on a golf course. The ball lands at point D as shown on the
diagram. Points A and D are on the same horizontal level.
–1
30m s
–1
20m s
A
D
The initial horizontal component of the velocity of the ball is 20 m s–1 and the initial vertical
component is 30 m s–1. The time of flight of the golf ball between point A and point D is 6.0 s.
Air resistance is negligible and the acceleration of free fall g = 10 m s–2.
Calculate
(a)
the maximum height reached by the golf ball.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(3)
(b)
the range of the golf ball.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(2)
(Total 5 marks)
61
56.
The graph below shows how a quantity y varies with time t for a falling object.
y
0
0
t
Which one of the following quantities could be represented by y?
A.
Speed when air resistance is negligible
B.
Speed when air resistance is not negligible
C.
Distance moved from rest when air resistance is negligible
D.
Distance moved from rest when air resistance is not negligible
(1)
62
57.
A stone is thrown with speed v from the top of a cliff of height H, as shown below.
h
v
cliff
H
sea
The stone is thrown at an angle to the horizontal so that it rises to a height h above the top of the
cliff before falling into the sea. The acceleration of free fall is g. Air resistance is negligible.
Which one of the following expressions gives correctly the speed of the stone as it hits the sea?
A.
v
2gh
B.
v
2gH 
C.
2g h  H 
D.
v
2
 2 gH

(1)
63
58.
A ball is thrown vertically upwards at time t = 0. Air resistance is not negligible and the
acceleration of free fall is g. The ball reaches a maximum height at time t = T and then
descends, reaching a terminal speed.
Which graph best shows the variation with time t of the acceleration a of the ball?
A. a
g
B. a
g
0
0
0
T
t
–g
–g
C. a
g
D. a
g
0
T
t
0
T
t
0
0
–g
0
T
t
–g
(1)
64
59.
The graph below shows the variation with time t of the displacement d of a body moving along
a straight-line.
d
0
0
t
Which graph best represents the variation with time t of the velocity v of this body?
A.
0
C.
B.
v
0
0
0
t
D.
v
0
t
v
0
t
0
t
v
0
(1)
65
60.
A body starting from rest moves along a straight-line under the action of a constant force. After
travelling a distance d the speed of the body is v.
initial position
v
d
The speed of the body when it has travelled a distance
A.
v
.
4
B.
v
.
2
C.
D.
v
2
d
from its initial position is
2
.
v
2 2
.
(1)
61.
Linear motion
(a)
Define the term acceleration.
...................................................................................................................................
...................................................................................................................................
(2)
66
(b)
An object has an initial speed u and an acceleration a. After time t, its speed is v and it
has moved through a distance s.
The motion of the object may be summarized by the equations
v = u + at,
s=
(i)
1
2
v  u t.
State the assumption made in these equations about the acceleration a.
.........................................................................................................................
(1)
(ii)
Derive, using these equations, an expression for v in terms of u, s and a.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
67
(c)
The shutter speed of a camera is the time that the film is exposed to light. In order to
determine the shutter speed of a camera, a metal ball is held at rest at the zero mark of a
vertical scale, as shown below. The ball is released. The shutter of a camera is opened as
the ball falls.
0 cm
scale
camera
196 cm
208 cm
The photograph of the ball shows that the shutter opened as the ball reached the 196 cm
mark on the scale and closed as it reached the 208 cm mark. Air resistance is negligible
and the acceleration of free fall is 9.81 m s–2.
(i)
Calculate the time for the ball to fall from rest to the 196 cm mark.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(ii)
Determine the time for which the shutter was open. That is, the time for the ball to
fall from the 196 cm mark to the 208 cm mark.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(Total 9 marks)
68
62.
This question is about projectile motion.
A stone is projected horizontally from the top of a cliff with a speed 15 m s–1.
15 m s–1
70 m
sea
The height of the cliff is 70 m and the acceleration of free fall is 10 m s–2. The stone strikes the
surface of the sea at velocity V.
(a)
Ignoring air resistance, deduce that the stone strikes the sea at a speed of 40 m s–1.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(2)
(b)
Use your answer in (a) to calculate the angle that the velocity V makes with the surface of
the sea.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(2)
(Total 4 marks)
69
63.
A ball rolls off a horizontal table with velocity v. It lands on the ground a time T later at a
distance D from the foot of the table as shown in the diagram below. Air resistance is negligible.
v
table
D
A second heavier ball rolls off the table with velocity v. Which one of the following is correct
for the heavier ball?
Time to land
Distance from table
A.
T
D
B.
T
less than D
C.
less than T
D
D.
less than T
less than D
(1)
70
64.
The graph shows the variation with time t of the acceleration a of an object.
20
15
a / ms
–2
10
5
0
0
1
2
3
4
5
6
7
8
9
10
t/s
The object is at rest at time t = 0.
Which of the following is the velocity of the object at time t = 6.0 s?
A.
0.50 m s–1.
B.
2.0 m s–1.
C.
36 m s–1.
D.
72 m s–1.
(1)
71
65.
An object is dropped from rest from a point several hundred metres above the surface of the
Earth at time t = 0. The object strikes the ground at t = T and air resistance is not negligible.
Which of the following sketch graphs best shows the variation with time t, of the speed v of the
object?
A.
B.
v
v
0
0
0
T
t
0
T
t
0
T
t
D.
C.
v
v
0
0
0
T
t
(1)
72
66.
Which of the following is a correct definition of average acceleration?
A.
change in velocit y
time taken
B.
velocity
time taken
C.
change in speed
time taken
D.
speed
time taken
(1)
73
67.
Motion of a ball
A ball of mass 0.25 kg is projected vertically upwards from the ground with an initial velocity
of 30 m s–1. The acceleration of free fall is 10 m s–2, but air resistance cannot be neglected.
The graph below shows the variation with time t of the velocity v of this ball for the upward part
of the motion.
v / ms–1
30.0
25.0
20.0
15.0
10.0
5.0
0.0
0.0
(a)
0.5
1.0
1.5
2.0
2.5
3.0
t/s
State what the area under the graph represents.
...................................................................................................................................
(1)
74
(b)
Estimate the maximum height reached by the ball.
...................................................................................................................................
...................................................................................................................................
(1)
(c)
Determine, for the ball at t = 1.0 s,
(i)
the acceleration;
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(3)
(ii)
the magnitude of the force of air resistance.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(d)
Use the graph to explain, without any further calculations, that the force of air resistance
is decreasing in magnitude as the ball moves upward.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(2)
75
(e)
The diagram below is a sketch graph of the upward motion of the ball.
Draw a line to indicate the downward motion of the ball. The line should indicate the
motion from the maximum height of the ball until just before it hits the ground.
v / ms–1 30
20
10
0.0
0.0
2.0
4.0
t/s
–10
–20
–30
(2)
(f)
State and explain, by reference to energy transformations, whether the speed with which
the ball hits the ground is equal to 30 m s–1.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(2)
(g)
Use your answer in (f) to state and explain whether the ball takes 2.0 s to move from its
maximum height to the ground.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(2)
(Total 15 marks)
76
68.
A projectile is fired from the ground at time t = 0. It lands back on the ground at time t = T.
Which of the following sketch graphs best shows the variation with time t of the vertical speed
VV and horizontal speed VH of the projectile? Air resistance is negligible.
A.
B.
VH
speed
VH
speed
VV
VV
0
0
T
0
t
0
T
t
T
t
D.
C.
speed
speed
VH
VV
0
0
VH
T
t
0
0
VV
(1)
77
69.
An object has initial speed u and acceleration a. After travelling a distance s, its final speed is v.
The quantities u, v, a and s are related by the expression
v2 = u2 + 2as.
Which of the following includes the two conditions necessary for the equation to apply?
A.
a has constant direction
u and v are in the same direction
B.
a has constant direction
a, u and v are in the same direction
C.
a has constant magnitude
a has constant direction
D.
a has constant magnitude
u and v are in the same direction
(1)
70.
This question is about projectile motion.
A ball is projected from ground level with a speed of 28 m s–1 at an angle of 30 to the
horizontal as shown below.
30
wall
h
16m
There is a wall of height h at a distance of 16 m from the point of projection of the ball. Air
resistance is negligible.
(a)
Calculate the initial magnitudes of
(i)
the horizontal velocity of the ball;
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(1)
78
(ii)
the vertical velocity of the ball.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(1)
(b)
The ball just passes over the wall. Determine the maximum height of the wall.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(3)
(Total 5 marks)
79
71.
Two forces P and Q act at a point X. The individual forces are represented in magnitude and
direction in the diagram below.
Which of the following diagrams best shows the value of S, where S = (P – Q)?
B.
A.
P
P
Q
S
S
Q
S
D.
C.
Q
Q
P
S
P
(1)
80
72.
Two identical metal spheres X and Y are released at the same time from the same height above
the horizontal ground. Sphere X falls vertically from rest. Sphere Y is projected horizontally as
shown below.
X
Y
ground
Air resistance is negligible.
Which of the following statements is correct?
A.
Sphere X hits the ground before sphere Y because it travels a shorter distance.
B.
Sphere Y hits the ground before sphere X because its initial velocity is greater.
C.
The spheres hit the ground at the same time because horizontal motion does not affect
vertical motion.
D.
The spheres hit the ground at the same time because they have equal weights.
(1)
81
73.
The graph below shows the variation with time t of the displacement s of an object moving
along a straight-line.
s/m
20.0
0.0
0.0
2.0
4.0 t / s
The best estimate of the instantaneous speed of the object at t = 2.0 s is
A.
0.0 ms–1.
B.
0.2 ms–1.
C.
5.0 ms–1.
D.
10.0 ms–1.
(1)
82
74.
This question is about circular motion.
A stone is attached to an inextensible string. The stone is made to rotate at constant speed v in a
horizontal circle. Diagram 1 below shows the stone in two positions A and B.
Diagram 1
Diagram 2
v
B
A
A
v
Diagram 2 above shows the velocity vector of the stone at point A.
(a)
On diagram 2, draw vectors to show the change in velocity v of the stone from point A
to point B.
(3)
(b)
Use your completed diagram 2 to explain why a force, directed towards the centre of the
circle, is necessary to cause circular motion.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(2)
(Total 5 marks)
83
75.
Linear motion
At a sports event, a skier descends a slope AB. At B there is a dip BC of width 12 m. The slope
and dip are shown in the diagram below. The vertical height of the slope is 41 m.
A
(not to scale)
slope
41m
C
B
D
1.8m
dip
12m
The graph below shows the variation with time t of the speed v down the slope of the skier.
25.0
20.0
v / ms –1
15.0
10.0
5.0
0.0
0.0
1.0
2.0
3.0
4.0 5.0
t/s
6.0
7.0
8.0
The skier, of mass 72 kg, takes 8.0 s to ski, from rest, down the length AB of the slope.
(a)
Use the graph to
(i)
calculate the kinetic energy EK of the skier at point B.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(ii)
determine the length of the slope.
84
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(4)
(b)
(i)
Calculate the magnitude of the change EP in the gravitational potential energy of
the skier between point A and point B.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(ii)
Use your anwers to (a)(i) and (b)(i) to determine the ratio
EP  EK  .
E P
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(iii)
Suggest what this ration represents.
.........................................................................................................................
.........................................................................................................................
(1)
85
(c)
At point B of the slope, the skier leaves the ground. He “flies” across the dip and lands on
the lower side at point D. The lower side C of the dip is 1.8 m below the upper side B.
(i)
Calculate the time taken for an object to fall, from rest, through a vertical distance
of 1.8 m. Assume negligible air resistance.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(ii)
The time calculated in (c)(i) is the time of flight of the skier across the dip.
Determine the horizontal distance travelled by the skier during this time, assuming
that the skier has the constant speed at which he leaves the slope at B.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(Total 15 marks)
86
76.
This question is about projectile motion.
The barrel of a rifle is held at an angle  to the horizontal. A bullet fired from the rifle leaves the
barrel at time t = 0 with a speed 200 m s–1. The graph below shows the variation with time t of
the vertical height h of the bullet.
600
500
400
300
h/m
200
100
0
0
5
10
15
20
25
t/s
(a)
Using the axes below, draw a sketch graph to show the variation of h with the horizontal
distance x travelled by the bullet. (Note: this is a sketch graph; you do not have to add
any values to the axes.)
h
x
(2)
(b)
State the expression for the initial vertical component of speed Vv in terms of the initial
speed of the bullet and the angle .
...................................................................................................................................
(1)
87
(c)
Use data from the graph to deduce that the angle  = 30. (The acceleration for free fall
g = 10 m s–2)
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(3)
(Total 6 marks)
77.
The graph below shows the variation with time t of the acceleration a of a body moving in a
straight-line.
a
0
0
t1
t2
t
The shaded area represents
A.
the change in velocity from t1 to t2.
B.
the velocity at t2.
C.
the average velocity between t1 and t2.
D.
the velocity at t1.
(1)
88
78.
A particle is projected horizontally with speed v from a height H. It lands a horizontal distance R
from the point of launch as shown in the diagram below.
v
H
R
A second particle is projected horizontally from the same height with speed 2v. Neglecting air
resistance the horizontal distance travelled by this particle is
A.
B.
R.
2R.
C.
2R.
D.
4R.
(1)
89
79.
Linear motion
At a sports event, a skier descends a slope AB. At B there is a dip BC of width 12 m. The slope
and dip are shown in the diagram below. The vertical height of the slope is 41 m.
A
(not to scale)
slope
41m
C
B
D
1.8m
dip
12m
The graph below shows the variation with time t of the speed v down the slope of the skier.
25.0
20.0
v / ms –1
15.0
10.0
5.0
0.0
0.0
1.0
2.0
3.0
4.0 5.0
t/s
6.0
7.0
8.0
The skier, of mass 72 kg, takes 8.0 s to ski, from rest, down the length AB of the slope.
90
(a)
Use the graph to
(i)
calculate the kinetic energy EK of the skier at point B.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(ii)
determine the length of the slope.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(4)
(b)
(i)
Calculate the change EP in the gravitational potential energy of the skier between
point A and point B.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(ii)
Use your answers to (a) and (b)(i) to determine the average retarding force on the
skier between point A and point B.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(3)
91
(iii)
Suggest two causes of the retarding force calculated in (ii).
1.
...............................................................................................................
2.
...............................................................................................................
(2)
(c)
At point B of the slope, the skier leaves the ground. He “flies” across the dip and lands on
the lower side at point D. The lower side C of the dip is 1.8 m below the upper side B.
Determine the distance CD of the point D from the edge C of the dip. Air resistance may
be assumed to be negligible.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(4)
(d)
The lower side of the dip is altered so that it is inclined to the horizontal, as shown below.
C
B
D
slope
1.8m
dip
12m
(i)
State the effect of this change on the landing position D.
.........................................................................................................................
.........................................................................................................................
(1)
92
(ii)
Suggest the effect of this change on the impact felt by the skier on landing.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(Total 20 marks)
80.
A small steel ball falls from rest through a distance of 3 m. When calculating the time of fall, air
resistance can be ignored because
A.
air is less dense than steel.
B.
air resistance increases with the speed of the ball.
C.
the air is not moving.
D.
air resistance is much less than the weight of the ball.
(1)
93
81.
The graph shows the variation with time t of the velocity v of an object moving along a straight
line.
v
0
0
t
Which graph shows the variation with time t of the acceleration a of the object?
a
A. a
B.
0
0
0
t
0
t
a
a
C.
D.
0
0
0
t
0
t
(1)
94
82.
Two identical metal spheres are held above the ground as shown.
spheres
(not to scale)
ground
The separation between them is small compared to their distance above the ground. When the
spheres are released, the separation of the spheres will
A.
remain constant.
B.
decrease continuously.
C.
increase continuously.
D.
increase initially and then remain constant.
(1)
83.
An object is falling, in air, towards the Earth’s surface.
What changes occur in the acceleration and in the velocity of the object as it approaches
terminal velocity?
acceleration
velocity
A.
decreases to zero
increases continuously
B.
decreases to zero
increases to a constant value
C.
constant
increases to a constant value
D.
constant
increases continuously
(1)
95
84.
This question is about projectile motion.
A ball is kicked at an angle to the horizontal. The diagram below shows the position of the ball
every 0.50 s.
30
25
20
vertical displacement / m
15
10
5
0
0
30
20
10
horizontal displacement / m
40
The acceleration of free fall is g = 10 m s–2. Air resistance may be neglected.
(a)
Using the diagram determine, for the ball
(i)
the horizontal component of the initial velocity.
...........................................................................................................................
...........................................................................................................................
(1)
(ii)
the vertical component of the initial velocity.
...........................................................................................................................
...........................................................................................................................
(2)
96
(iii)
the magnitude of the displacement after 3.0 s.
...........................................................................................................................
...........................................................................................................................
(2)
(b)
On the diagram above draw a line to indicate a possible path for the ball if air resistance
were not negligible.
(2)
(Total 7 marks)
85.
A stone is thrown from the top of a cliff with speed v at an angle θ above the horizontal, as
shown.
cliff
Air resistance is negligible and the acceleration of free fall is g.
What is the horizontal velocity of the stone a time t after the stone has been thrown?
A.
v sinθ
B.
v sinθ – gt
C.
v cosθ
D.
v cosθ – gt
(1)
97
This question is about projectile motion.
A stone is thrown from the top of a cliff of height 28 m above the sea. The stone is thrown at a
speed of 14 m s–1 at an angle above the horizontal. Air resistance is negligible.
14 m s–1
...........
86.
28m
sea
The maximum height reached by the stone measured from the point from which it is thrown is
8.0 m.
(a)
By considering the energy of the stone, determine the speed with which the stone hits the
sea.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
98
(b)
The stone leaves the cliff at time t = 0. It reaches its maximum height at t = TH. On the
axis below, draw a sketch-graph to show the variation with time t of the magnitude of the
vertical component of velocity of the stone from t = 0 to t = TS, the time just before the
stone strikes the sea.
speed
0
0
t
TH
TS
(4)
(Total 7 marks)
87.
A car has a speed of + 15 m s–1 relative to the ground. It passes a cyclist travelling in the same
straight-line. The speed of the car relative to the cyclist is + 12 m s–1.
The speed of the cyclist relative to the ground is
A.
–3.0 m s–1.
B.
–1.5 m s–1.
C.
+1.5 m s–1.
D.
+3.0 m s–1.
(1)
99
88.
A steel sphere is dropped from rest in oil. Which of the following graphs best represents the
variation with time of the speed of the sphere?
A.
speed
B.
0
0
0
C.
speed
time
speed
D.
0
0
time
0
time
speed
0
0
time
(1)
100
89.
This question is about projectile motion.
A projectile is fired horizontally from the top of a vertical cliff of height 40 m.
projectile
cliff
40 m
sea
At any instant of time, the vertical distance fallen by the projectile is d. The graph below shows
the variation with distance d, of the kinetic energy per unit mass E of the projectile.
1400
1300
1200
E / J kg –1
1100
1000
900
800
0
5
10
15
20
d/m
25
30
35
40
101
(a)
Use data from the graph to calculate, for the projectile,
(i)
the initial horizontal speed.
...........................................................................................................................
(1)
(ii)
the speed with which it hits the sea.
...........................................................................................................................
(1)
(b)
Use your answers to (a) to calculate the magnitude of the vertical component of velocity
with which the projectile hits the sea.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(Total 4 marks)
90.
The graph below shows the variation with time t of the acceleration a of an object from t = 0 to
t = T.
a
0
0
T
t
The shaded area under the graph represents change in
A.
displacement.
B.
velocity.
C.
momentum.
D.
kinetic energy.
(1)
102
91.
The diagram below shows the trajectory of a ball thrown into the air. There is no air resistance.
trajectory of ball
X
A
B
C
D
Which arrow gives the direction of the resultant force on the ball at the point X?
A.
A
B.
B
C.
C
D.
D
(1)
103
92.
A ball is thrown vertically upwards from the ground. The graph shows the variation with time t
of the vertical displacement d of the ball.
Which of the following gives the final displacement after time T and the average speed between
time t = 0 m aand time t = T?
A.
B.
C.
D.
Displacement
Average speed
0
0
0
2D
T
2D
2D
T
2D
0
(1)
104
93.
The graph below shows the variation with time t of the velocity v of an object moving on a
straight-line.
Which of the graphs below best represents the variation with time t of the acceleration a of the
object?
(1)
105
94.
This question is about throwing a stone from a cliff.
Antonia stands at the edge of a vertical cliff and throws a stone vertically upwards.
The stone leaves Antonia’s hand with a speed v =8.0 m s–1. Ignore air resistance, the
acceleration of free fall g is 10 m s–2 and all distance measurements are taken from the point
where the stone leaves Antonia’s hand.
(a)
Determine,
(i)
the maximum height reached by the stone.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(2)
(ii)
the time taken by the stone to reach its maximum height.
.........................................................................................................................
.........................................................................................................................
(1)
106
(b)
The time between the stone leaving Antonia’s hand and hitting the sea is 3.0 s. Determine
the height of the cliff.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
(3)
(Total 6 marks)
107