Physics 30S
Kinematics Review
1. (a) What is acceleration? (b) Why is the unit of time squared in measuring acceleration?
2. How do the directions of an acceleration vector and its corresponding velocity vector compare
for the uniformly accelerated linear motion of an object starting from rest?
3. Define the following: a) uniform acceleration b) variable acceleration c) uniform deceleration
d) variable deceleration
4. If a ball is dropped and attains a velocity of 29.31 m/s in 3.00 s, what is the acceleration due to
gravity?
5. An automobile can be accelerated from 95 km/hr to 142 km/hr in 8.1s. What is the
acceleration
6. The position-time graph of a car travelling along a road is shown in the figure below. Make a
graph of its velocity versus time.
position (km)
7. Sue rode her bicycle as fast as she could from her house to Anne’s house. After a short time
she rode back as fast as she
position vs time
could. The figure shows a
position-time graph of her
8
trip. From the information
given and your graph, what
6
would your give as a
plausible description of the
4
road between Sue’s house
and Anne’s house?
2
8. What is the displacement of
a car which travels at a
steady velocity of 60 km/h
a) for 3 hours
b) for 1/2 hour
0
0
0.2
0.4
0.6
0.8
time (hours)
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1
1.2
1.4
1.6
Physics 30S
Kinematics Review
9. A man walks to the corner to mail a letter and comes back. Sketch graphs showing his
velocity and position plotted against time.
10. Car A is stopped at a traffic light. The light turns green and A starts up. Just as it does so,
B passes it, going at a steady velocity. Their velocity-time curves are shown below.
a.
b.
c.
d.
e.
How long does it take car A to be going as fast as car B?
At that time, how much is car B ahead of car A?
Which car is ahead, and by how much, at the end of 0.012 hour?
At what time does car A catch up with car B? BONUS
How far have they traveled from the traffic light by the time car A catches up?
BONUS
11. The accompanying data show the instantaneous velocity of a car at intervals of 1 second. Plot
the velocity versus time, and use your graph to answer the following questions.
a. How fast is the car going at 2.6 s? At 4.8 s?
b. How far did the car travel between the two instants in part (a)?
TIME (s)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
VELOCITY (m/s)
10.0
12.4
14.8
17.2
19.6
22.0
24.4
12. A car is traveling along a road at a constant velocity. It passes an unmarked police car
parked beside the road. The police car accelerates, overtakes the speeding car, passes it,
and signals it to a stop. Sketch a graph showing the velocities of the two cars plotted
against time.
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Physics 30S
Kinematics Review
13. Sketch a velocity-time graph for a ball thrown straight up from the time it is still at rest in
the hand till it is momentarily at rest on the ground. (b) Should the area between the curve
and the time axis above time axis be equal to the
corresponding area below the time
axis? (c) Use the graph in (a) to sketch the acceleration-time graph for the same motion.
14. Does a car speedometer measure speed, velocity or both?
15. If an accurate speedometer registers a constant value for a period of time, can you
determine the average velocity over the period of time using only the speedometer?
Explain.
16. Can the average velocity of a particle be zero over a given time interval if it is not zero
over a shorter time interval? Explain.
17. Can an object have a varying velocity if its speed is constant? If yes, give examples.
18. Can an object have a varying speed if its velocity is constant? If yes, give examples.
19. When an object moves with constant velocity, does its average velocity during any time
interval differ from its instantaneous velocity at any instant?
20. Compare the acceleration of a motorcycle that accelerates from 80 km/h to 90 km/h with
the acceleration of a bicycle that accelerates from rest to 10km/h in the same time.
21. Can you conclude that a car is not accelerating if its speedometer indicates a steady
60km/h
22. Can an object have a northward velocity and a southward acceleration? Explain.
23. Can the velocity of an object be negative when its acceleration is positive? What about
vice versa?
24. Give an example where both the velocity and acceleration are negative.
25. A rock is thrown vertically upward with speed v from the edge of a cliff. A second rock is
thrown vertically downward with the same initial speed. Which rock has the greater speed
when it reaches the bottom of the cliff? Ignore air resistance.
26. A ball, thrown vertically upward, returns to the thrower’s hand. Which part of the journey
requires the longer time, upward or downward? Answer for (a) no air resistance and (b) in
the presence of air resistance. {Hint the acceleration due to air resistance is always in a
direction opposite to the motion.
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Physics 30S
Kinematics Review
27. Describe in words the motion plotted in the figure.
28. Describe in words the motion of the object graphed in the figure.
29. What must be your average speed in order to travel 220 km in 2.25h?
30. At an average speed of 31.0km/h, how far will a bicyclist travel in 135 min?
31. A bird can fly 30 km/h. How long does it take to fly 22 km?
32. If you are driving 100km/h and you look to the side for 2.0s, how far do you travel during
this inattentive period?
33. A person jogs eight complete laps around a quarter mile track in a total time of 13.5 min.
Calculate (a) its average speed and (b) its average velocity.
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Physics 30S
Kinematics Review
34. A dog runs 100m away from its master in a straight line in 8.4s, and then runs halfway
back in one-third the time. Calculate (a) its average speed and (b) its average velocity.
35. An airplane travels 2100 km at a speed of 1000 km/h. In then encounters a headwind that
slows it to 800km/h for the next 1300km. What was the average speed of the plane for
this trip?
36. A sports car accelerates from rest to 100 km/h in 6.6s. What is its acceleration in m/s2?
37. At highway speeds, a particular automobile is capable of an acceleration of about 1.7m/s2.
At this rate, how long does it take to accelerate from 85 km/h to 100 km/h?
38. The position of a racing car, which starts from rest at t = 0 and moves in a straight line, has
been measured as a function of time, as given in the following table. Estimate (a) its
velocity and (b) its acceleration as a function of time. Display each in a table and on a
graph.
Time (s)
Posn (m)
Time
(s)
Posn
(m)
0
0
0.25
0.11
0.50
0.46
0.75
1.06
1.00
1.94
1.50
4.62
2.50
3.00
3.50
4.00
4.50
5.00
5.50
6.00
13.79
20.36
28.31
37.65
48.37
60.30
73.26
87.16
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2.00
8.55
Physics 30S
Kinematics Review
Answers:
1) Acceleration is the rate of change of velocity with respect to time. b) The units of acceleration
are the units of velocity, m/s, divided by the unit of time, s, m/s2
2) They act along the same line, and they have the same direction.
3) (a) Uniform acceleration is motion for which the velocity curve in a velocity-time graph is a
straight line, and its slope is positive.
(b) For variable acceleration, the velocity curve is not a straight line, but its slope is always
positive.
(c) The velocity curve is a straight line with a negative slope.
(d) The velocity curve is not a straight line, but its slope is always negative.
v
a
t
29.31
4) a 
3
a  9.77m / s2
5) 142 ÷ 3.6 = 39.4 m/s
95 ÷ 3.6 = 26.2 m/s
v
a
t
39.4  26.4
a
8.1
a  1.6m / s 2
6)
7) From the velocity-time graph and the position-time graph we see that on the first part of the
trip Sue’s speed was 12.5 km/h; on the way back her speed on the way back her speed on the
same part was 25.0 km/h. This suggests a slight upgrade on the way out. On the second part
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Physics 30S
Kinematics Review
her speed was 30km/h, and on the way back it was only 6km/h. This suggests a downgrade on
the way out, which is larger in magnitude than the upgrade in the first part.
8) 180 km
(b) 30 km
9) velocity vs. time
position vs. time
6
12
4
10
2
velocity
8
0
6
-2
-4
4
-6
2
-8
0
0
time
10)
2
4
6
8
Car A vs. Car B
a) The velocity-time graphs for the cars cross at t = 0.0048h, so at this time the two cars
have the same speed.
b) Car B has moved 60km/h x 0.0048 h = 0.29 km
Car A has moved 1/2 x 60 km/h x 0.0048 h = 0.14 km.
Hence car B is 0.15 km ahead of Car A.
c) Car B has moved 60 km/h x 0.012 h= 0.72 km.
Car A has moved 1/2 x 100 x 0.008 + 100 x (0.012-0.008) = 0.80 km.
Hence Car A is ahead by 0.08 km.
d) Car A catches up with car B when both have traveled the same distance. Let t be be the
time at which this happens.
Car B travels 60 t km.
Car A travels 1/2 x 100 x 0.008 – 100 x (t-0.008) km.
Then 60 t = 0.40 + 100 t –0.80and t = 0.01 h.
(You can see that car A catches up with car B at some time after t = 0.008 h. for by
this time car B has traveled 0.008 h x 60 km/h or 0.48 km while car A has traveled 1/2 x
100km/h x 0.008 h or 0.40 km)
e) Car B has traveled 60 km/h x 0.01 h = 0.60km.
Car A has traveled the same distance.
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Physics 30S
Kinematics Review
11)
a) 16 m/s
21 m/s
vi  v f
d
v
v
t
2
d
16  21
18.5 
b) v 
(4.8  2.6)
2
v  18.5m / s
d  18.5(4.8  2.6)
d  40.7m
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Physics 30S
Kinematics Review
12) The police car must travel the same total distance as the other car in order to pass it and must
therefore accelerate to a higher speed. The area OCDT, which represents the distance traveled
by the police car when it has reached the point at which it passes the speeder, equals the area
OABT, which represents the distance traveled by the speeder. After the police car has
signaled, the two cars come to zero speed at the same distance. The areas PDT and KBT must
be equal.
There are other solutions, such as: OABT = OC’D’BT after which both cars stop at the same
time K.
13)
a)
b) Almost; the distance the ball rises must equal the distance the ball has fallen as it passes
the thrower’s hand, and it will fall the additional distance representing the height of the
thrower’s hand above the ground.
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Physics 30S
Kinematics Review
c)
29. 97.8 km/h
31. 0.73h
33. (a) 89 km/h (b) 25 m/s (c) 81 ft/s
35. (a) 3.97 m/s (b) 0 m/s
37. 913 km/h
39. 6.73 m/s
41. 2.5s
(a) 0.44m/s, 1.4m/s, etc.
(b) 3.8 m/s2, 4.0 m/s2 , etc.
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