Regents Physics – Midterm Review Free Response Name _________
1. The graph below shows the relationship between speed and elapsed time for a car moving in
a straight line.
a. Determine the magnitude of the acceleration of the car. [1]
a = slope = 1.25 m/s/s
b. Calculate the total distance the car traveled during the time interval 4.0 seconds to 8.0
seconds. [Show all work, including the equation and substitution with units.] [2]
d = vit +1/2 at2 = (5 m/s)(4 s) + (1/2)(1.25 m/s/s)(4 s)2 = 30 m
1
Regents Physics – Midterm Review Free Response Name _________
2. A 28-gram rubber stopper is attached to a string and whirled clockwise in a horizontal circle
with a radius of 0.80 meter. The diagram in your answer booklet represents the motion of the
rubber stopper. The stopper maintains a constant speed of 2.5 meters per second.
a. Calculate the magnitude of the centripetal acceleration of the stopper. [Show all work,
including the equation and substitution with units.] [2]
ac = v2/r = (2.5 m/s)2 / (0.8 m) = 7.8 m/s2
b. On the diagram, draw an arrow showing the direction of the centripetal force acting on
the stopper when it is at the position shown. [1]
3. A projectile is fired with an initial velocity of 120. meters per second at an angle, θ,
above the horizontal. If the projectile’s initial horizontal speed is 55 meters per second.
What is the measurement of angle θ?
θ = cos-1(55 m/s / 120 m/s) = 63o
4. Calculate the magnitude of the centripetal force acting on Earth as it orbits the Sun,
assuming a circular orbit and an orbital speed of 3.00 × 104 meters per second. [Show all
work, including the equation and substitution with units.] [2]
Fc = mv2/r = (5.98 kg x 1024)(3.00 x 104 m/s)2 / (1.5 x 1011 m) = 3.6 x 1022 N
2
Regents Physics – Midterm Review Free Response Name _________
5. A student produced various elongations of a spring by applying a series of forces to the
spring. The graph below represents the relationship between the applied force and the
elongation of the spring.
a. Determine the spring constant of the spring. [1]
k = F / x = 20 N/m
b. Calculate the energy stored in the spring when the elongation is 0.30 meter. [Show all
work, including the equation and substitution with units.] [2]
PEs = (1/2) kx2 = (1/2)(20 N/m)(0.3 m)2 = 0.9 J
6. A projectile is launched at an angle above the ground. The horizontal component of the
projectile’s velocity, vx, is initially 40. meters per second. The vertical component of the
projectile’s velocity, vy, is initially 30. meters per second. What are the components of the
projectile’s velocity after 2.0 seconds of flight? [Neglect friction.][1]
vx = constant = 40 m/s
vy = viy + at = 30 m/s + (-9.81 m/s2) (2.0 s) = 10. m/s
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Regents Physics – Midterm Review Free Response Name _________
7. A girl rides her bicycle 1.40 kilometers west, 0.70 kilometer south, and 0.30 kilometer east in
12 minutes. The vector diagram in your answer booklet represents the girl’s first two
displacements in sequence from point P. The scale used in the diagram is 1.0 centimeter
0.20 kilometer.
a. On the vector diagram, using a ruler and a protractor, construct the following vectors:

Starting at the arrowhead of the second displacement vector, draw a vector to represent
the 0.30 kilometer east displacement. Label the vector with its magnitude. [ 1]

Draw the vector representing the resultant displacement of the girl for the entire bicycle
trip and label the vector R. [1]
b. Calculate the girl’s average speed for the entire bicycle trip. [Show all work, including
the equation and substitution with units.] [2]
v = d / t = (1.40 km + 0.70 km + 0.30 km) / 12 min = 0.2 km / min
c. Determine the magnitude of the girl’s resultant displacement for the entire bicycle trip, in
kilometers. [1]
1.3 km
d. Determine the measure of the angle, in degrees, between the resultant and the 1.40kilometer displacement vector. [1]
27o
4
Regents Physics – Midterm Review Free Response Name _________
8. A 30.4-newton force is used to slide a 40.0-newton crate a distance of 6.00 meters at constant
speed along an incline to a vertical height of 3.00 meters.
a. Determine the total work done by the 30.4-newton force in sliding the crate along the
incline. [1]
W = Fdcosθ = (30.4 N)(6.00 m)cos0o = 182 J
b. Calculate the total increase in the gravitational potential energy of the crate after it has
slid 6.00 meters along the incline. [Show all work, including the equation and substitution
with units.] [2]
PE = mgh = (40 N)(3.0 m) = 120 J
c. State what happens to the kinetic energy of the crate as it slides along the incline. [ 1]
Kinetic energy is constant because the speed is constant
d. State what happens to the internal energy of the crate as it slides along the incline. [1]
Internal energy of the crate is increasing as it slides along the incline.
9. A skier starting from rest skis straight down a slope 50. meters long in 5.0 seconds. What
is the magnitude of the acceleration of the skier? [Show all work, including the equation
and substitution with units.] [2]
d = vit + (1/2)at2
50 m = (0 m/s)(5.0 s) + (1/2) a (5.0 s)2
a = 4 m/s2
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Regents Physics – Midterm Review Free Response Name _________
10. A machine launches a tennis ball at an angle of 45° with the horizontal, as shown. The
ball has an initial vertical velocity of 9.0 meters per second and an initial horizontal
velocity of 9.0 meters per second. The ball reaches its maximum height 0.92 second after
its launch. [Neglect air resistance and assume the ball lands at the same height above the
ground from which it was launched.]
a. What is the speed of the tennis ball as it leaves the launcher? [1]
2
vi  vix  viy  (9.0m / s) 2  (9.0m / s) 2  13m / s
2
b. What is the total horizontal distance traveled by the tennis ball during the entire time
it is in the air? [Show all work, including the equation and substitution with units.] [2]
dx = vixt = (9.0 m/s) (0.92 s ∙ 2) = 17 m
11. A child kicks a ball with an initial velocity of 8.5 meters per second at an angle of 35º
with the horizontal, as shown in the diagram. The ball has an initial vertical velocity of
4.9 meters per second and a total time of flight of 1.0 second. [Neglect air resistance.]
What is the maximum height reached by the ball? [Show all work, including the equation
and substitution with units.] [2]
v fy  viy  2a y d y
2
2
(0m / s)2  (4.9m / s) 2  2(9.81m / s 2 )d y
d y  1.2m
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Regents Physics – Midterm Review Free Response Name _________
12. A soccer ball is kicked from point Pi at an angle above a horizontal field. The ball
follows an ideal path before landing on the field at point Pf .
a. On the above diagram, draw an arrow to show the direction of the net force on the
ball when it is at position X? [Neglect friction.] [1]
b. On the above diagram, draw an arrow to show the direction of acceleration on the ball
when it is at position Y? [Neglect friction.] [1]
13. As shown in the diagram below, a student standing on the roof of a 50.0-meter-high
building kicks a stone at a horizontal speed of 4.00 meters per second. How much time is
required for the stone to reach the level ground below? [Neglect friction.][1]
1
d y  viy t  a y t 2
2
1
 50m  (0m / s )(t )  ( )( 9.81m / s 2 )t 2
2
t  3.2s
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Regents Physics – Midterm Review Free Response Name _________
14. A machine fired several projectiles at the same angle, θ, above the horizontal. Each
projectile was fired with a different initial velocity, vi. The graph below represents the
relationship between the magnitude of the initial vertical velocity, viy, and the magnitude
of the corresponding initial velocity, vi, of these projectiles. Determine the angle, θ, above
the horizontal at which the projectiles were fired. [Show all work, including the equation
and substitution with units.] [2]
viy  vi sin 
25m / s  (40m / s ) sin 
25m / s
  sin 1 (
)  39 o
40m / s
15. Base your answer to the question on the graph below, which represents the relationship
between velocity and time for a car moving along a straight line, and your knowledge of
physics.
a. Determine the magnitude of the car’s acceleration during the first 6.0 seconds.[1]
a = slope = 2.5 m/s2
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Regents Physics – Midterm Review Free Response Name _________
b. Determine the magnitude of the average velocity of the car from t = 6.0 seconds to t =
10. seconds.[1] 15m/s
16. A truck, initially traveling at a speed of 22 meters per second, increases speed at a
constant rate of 2.4 meters per second2 for 3.2 seconds. What is the total distance traveled
by the truck during this 3.2-second time interval?[1]
1
d  vi t  at 2
2
1
d  (22m / s )(3.2 s )  (2.4m / s 2 )(3.2 s ) 2  83m
2
17. What are the horizontal and vertical components of a 15-meters-per-second velocity at an
angle of 60.° above the horizontal? [2]
v x  v cos  (15m / s) cos 60 o  7.5m / s
vy  v sin   (15m / s) sin 60o  13m / s
18. A car traveling west in a straight line on a highway decreases its speed from 30.0 meters
per second to 23.0 meters per second in 2.00 seconds. What is the car’s average
acceleration during this time interval? [2]
v 23.0m / s  30.0m / s
a

 3.50m / s 2
t
2.00 s
19. If a 30-newton force is required to accelerate a 2-kilogram object at 10 meters per
second2, over a level floor, what is the magnitude of the frictional force acting on the
object? [1]
Fnet  Fapp  F f
ma  Fapp  F f
(2kg)(10m / s 2 )  30 N  F f
F f  10 N
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Regents Physics – Midterm Review Free Response Name _________
20. A 10.-kilogram box, sliding to the right across a rough horizontal floor, accelerates at -2.0
meters per second2 due to the force of friction.
a. Calculate the magnitude of the net force acting on the box.[1]
Fnet  ma  (10kg)( 2.0m / s 2 )
Fnet  20 N
b. Calculate the coefficient of kinetic friction between the box and the floor. [Show all work,
including the equation and substitution with units.] [2]
F f  FN
20 N   (10kg)(9.81m / s 2 )
  0.2
21. A 1.2 × 103-kilogram automobile in motion strikes a 1.0 × 10-4-kilogram insect. As a
result, the insect is accelerated at a rate of 1.0 × 102 m/s2. What is the magnitude of the
force the insect exerts on the car? [Show all work, including the equation and substitution
with units.] [2]
Fnet  ma  (1.0 10 4 kg)(1.0 10 2 m / s 2 )
Fnet  0.01N
22. A horizontal 20.-newton force is applied to a 5.0-kilogram box to push it across a rough,
horizontal floor at a constant velocity of 3.0 meters per second to the right. Determine the
magnitude of the force of friction acting on the box.[1] 20 N
23. A 4.0-kilogram object is accelerated at 3.0 meters per second2 north by an unbalanced
force. What will be the acceleration on a 2.0 kg object if the same unbalanced force
acting on it?[1]
6 m/s2
24. A 0.50-kilogram puck sliding on a horizontal shuffleboard court is slowed to rest by a
frictional force of 1.2 newtons. What is the coefficient of kinetic friction between the
puck and the surface of the shuffleboard court? [Show all work, including the equation and
substitution with units.] [2]
Ff  FN
1.2 N   (0.50kg)(9.81m / s 2 )
  0.24
10
Regents Physics – Midterm Review Free Response Name _________
25. A student and the waxed skis he is wearing have a combined weight of 850 newtons. The
skier travels down a snow-covered hill and then glides to the east across a snow-covered,
horizontal surface. Calculate the magnitude of the force of friction acting on the skis as
the skier glides across the snow-covered, horizontal surface. [Show all work, including the
equation and substitution with units.] [2]
F f  FN
F f  (0.05)(850 N )  42.5 N
26. An ice skater applies a horizontal force to a 20.-kilogram block on frictionless, level ice,
causing the block to accelerate uniformly at 1.4 meters per second2 to the right. After the
skater stops pushing the block, it slides onto a region of ice that is covered with a thin
layer of sand. The coefficient of kinetic friction between the block and the sand-covered
ice is 0.28. Calculate the magnitude of the force of friction acting on the block as it slides
over the sand-covered ice. [Show all work, including the equation and substitution with
units.] [2]
Ff  FN
Ff  (0.28)(20kg)(9.81m / s 2 )  55N
27. A 1.0 × 103 kilogram car travels at a constant speed of 20. meters per second around a
horizontal circular track. The diameter of the track is 1.0 × 102 meters. What is the
magnitude of the car’s centripetal acceleration? [Show all work, including the equation and
substitution with units.] [2]
ac 
v 2 (20m / s) 2

 8m / s 2
r
50m
28. A 3.0-kilogram object is acted upon by an impulse having a magnitude of 15
newton•seconds. What is the magnitude of the object’s change in momentum due to this
impulse?[1] ∆p = J = 15 N∙s
29. An 8.0-kilogram cart moving to the right at 4.0 meters per second about to make a headon collision with a 4.0-kilogram cart moving to the left at 6.0 meters per second. After
the collision, the 4.0-kilogram cart moves to the right at 3.0 meters per second. What is
the velocity of the 8.0-kilogram cart after the collision? [Show all work, including the
equation and substitution with units.] [2]
m1v1  m2 v2  m1v1 ' m2 v2 ' (8.0kg)( 4.0m / s)  (4.0kg)( 6.0m / s)  (8.0kg)v1 '(4.0kg)(3.0m / s)
v1 '  0.5m / s
30. A student on an amusement park ride moves in a circular path with a radius of 3.5 meters
once every 8.9 seconds. What is the students average speed? [1]
d 2r 2 (3.5m)
v 

 2.5m / s
t
T
8.9 s
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Regents Physics – Midterm Review Free Response Name _________
31. In an experiment, a 0.028-kilogram rubber stopper is attached to one end of a string. A
student whirls the stopper overhead in a horizontal circle with a radius of 1.0 meter. The
stopper completes 10 revolutions in 10 seconds.
a. Calculate the magnitude of the centripetal force on the whirling stopper. [Show all
work, including the equation and substitution with units.] [2]
v
d 2r 2 (1m)


 6.24m / s
t
T
1s
Fc  mac  (0.028m / s)
(6.24m / s) 2
 1.1N
1m
b. Determine the speed of the whirling stopper.[1] 6.24m/s
32. A 0.149-kilogram baseball, initially moving at 15 meters per second, is brought to rest in
0.040 second by a baseball glove on a catcher’s hand. What is the magnitude of the
average force exerted on the ball by the glove?
F  ma  (0.149kg)
(0m / s  15m / s )
 56 N
0.040s
33. On a snow-covered road, a car with a mass of 1.1 × 103 kilograms collides head-on with a
van having a mass of 2.5 × 103 kilograms traveling at 8.0 meters per second. As a result
of the collision, the vehicles lock together and immediately come to rest. Calculate the
speed of the car immediately before the collision. [Neglect friction.]
m1v1  m2 v2  m1v1 ' m2 v2 ' (1.1  103 kg)(v1 )  (2.5  103 kg)(8.0m / s)  0
v1  18m / s
34. A 1200-kilogram car moving at 12 meters per second collides with a 2300-kilogram car
that is waiting at rest at a traffic light. After the collision, the cars lock together and slide.
Eventually, the combined cars are brought to rest by a force of kinetic friction as the
rubber tires slide across the dry, level, asphalt road surface. Calculate the speed of the
locked-together cars immediately after the collision.
m1v1  m2 v2  m1v1 ' m2 v2 ' (1200kg)(12m / s)  (2300kg)(0m / s)  (3500kg)v'
v1  4.1m / s
35. Calculate the magnitude of the impulse applied to a 0.75-kilogram cart to change its
velocity from 0.50 meter per second east to 2.00 meters per second east.
J  p  mv  (0.75kg)( 2.00m / s  0.50m / s)  1.13kg  m / s
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Regents Physics – Midterm Review Free Response Name _________
36. When Earth and the Moon are separated by a distance of 3.84 × 108 meters, the
magnitude of the gravitational force of attraction between them is 2.0 × 1020 newtons.
What would be the magnitude of this gravitational force of attraction if Earth and the
Moon were separated by a distance of 1.92 × 108 meters?
Since distance halved, Fg will quadruple. Fg = 8.0x1020 N
37. Io (pronounced “EYE oh”) is one of Jupiter’s moons discovered by Galileo. Io is slightly
larger than Earth’s Moon. The mass of Io is 8.93 × 1022 kilograms and the mass of Jupiter
is 1.90 × 1027 kilograms. The distance between the centers of Io and Jupiter is 4.22 × 108
meters.
a. Calculate the magnitude of the acceleration of Io due to the gravitational force
exerted by Jupiter.[1]
g
Fg
m

6.35 10 22 N
 0.711m / s 2
22
8.93 10 kg
b. Calculate the magnitude of the gravitational force of attraction that Jupiter exerts on
Io.[1]
Fg 
Gm1m2 (6.67  10 11 Nm2 / kg 2 )(8.93  10 22 kg)(1.90  10 27 kg)

 6.35  10 22 N
2
8
2
r
(4.22  10 m)
38. Two bowling balls, A and B, each having a mass of 7.00 kilograms, placed 2.00 meters
apart. What is the magnitude of the gravitational force exerted by ball A on ball B?[1]
8.2x10-10 N
39. The weight of an object was determined at five different distances from the center of
Earth. The results are shown in the table below. Position A represents results for the
object at the surface of Earth. The mass of Earth is 5.98 x 1024 kg.
a. What is the mass of the object? [1]
100 kg
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Regents Physics – Midterm Review Free Response Name _________
b. At what distance from the center of Earth is the weight of the object approximately 28
newtons? [2]
Gm1m2
r2
(6.67 10 11 Nm 2 / kg 2 )(5.98 10 24 kg)(100kg)
28 N 
r2
Fg 
r  3.77 10 7 m
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