Velocity & Acceleration
Force, Motion, and Energy
Part I: Speed and Velocity
Speed is a scalar quantity that refers to how fast an object is moving. Velocity is a vector quantity
that refers to the speed of an object in a specific direction. Essentially, velocity is speed in a
specific direction.
Average speed is often calculated using the following formula:
Average speed (s) = Total distance traveled (d) / Total time of travel (t)
Average velocity is often calculated using the following formula:
Average velocity (v) = Displacement (meters) / Time (sec)
1. Based on the units given for displacement and time, what will the units for velocity be?
2. During summer vacation, Juan traveled a total distance of 400 miles. His trip took 8 hours.
What was the average speed during the trip?
3. An alert driver can apply the brakes fully in about 0.5 seconds. How far would the car travel
moving at a rate of 29.06 m/s?
4. In 2013, the average time men in the United States could run a marathon was about 4 hours
and 16 minutes. If a marathon is 26.2 miles, what was the average speed?
5. In the same year, the average finishing time for U.S. women was 4 hours and 41 minutes.
What was the average female speed in miles per hour?
Part II: Acceleration
Acceleration is the rate an object changes its velocity. It is a vector quantity, meaning it has a
direction. The average acceleration of an object is the change in velocity over a given amount of
time. It can be calculated using the formula:
Average acceleration = Change in velocity (Δv) / Time (t)
1. If the velocity of a moving car increases from 9 m/s to 25 m/s in the span of 5 seconds, what
is the average acceleration during this time period?
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Velocity & Acceleration
Force, Motion, and Energy
2. Usain Bolt, the Olympian from Jamaica, is the fastest human ever recorded. Determine his
average rate of acceleration if he achieved a speed of 10.4 m/s in 9.58 sec. (Think about
what the initial speed of a sprinter is.)
Use the following information to answer questions 3–5. The following data was taken from a
manufacturer’s test for a car’s ability to accelerate and brake.
Plot the following sets of data on the graph provided.
Time (s)
0
2
4
6
8
10
12
14
16
18
20
22
Speed (m/s)
0
10
18
25
30
36
40
44
46
48
50
52
Time (s)
24
26
28
30
32
34
36
38
40
42
44
46
Speed (m/s)
55
55
55
55
55
55
55
55
55
35
15
0
3. Write a short description about what the graph shows.
4. What was the average acceleration during the time between 24 sec. and 40 sec.?
5. What was the average acceleration from 40 sec. to 46 sec.?
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