Calculating Acceleration from
Velocity and Time
Jean Brainard, Ph.D.
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Printed: March 2, 2014
AUTHOR
Jean Brainard, Ph.D.
www.ck12.org
C ONCEPT
Concept 1. Calculating Acceleration from Velocity and Time
1
Calculating Acceleration
from Velocity and Time
• Explain how to calculate average acceleration when direction is constant.
• Identify the SI unit for acceleration.
• Solve simple acceleration problems.
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This cyclist is in constant motion as he competes in an off-road mountain bike race. Both his speed and his direction
keep changing. Velocity is a measure that represents both speed and direction. Changes in velocity are measured by
acceleration. Acceleration reflects how quickly velocity is changing. It may involve a change in speed, a change in
direction, or both. You can see off-road bikers accelerating in these ways in the exciting mountain bike race at this
URL: http://vimeo.com/1630019
Calculating Average Acceleration in One Direction
Calculating acceleration is complicated if both speed and direction are changing or if you want to know acceleration
at any given instant in time. However, it’s relatively easy to calculate average acceleration over a period of time
when only speed is changing. Then acceleration is the change in velocity (represented by ∆v) divided by the change
in time (represented by ∆t):
acceleration =
∆v
∆t
Accelerating on a Bike
Look at the cyclist in the Figure 1.1. With the help of gravity, he speeds up as he goes downhill on a straight part of
the trail. His velocity changes from 1 meter per second at the top of the hill to 6 meters per second by the time he
reaches the bottom. If it takes him 5 seconds to reach the bottom, what is his average acceleration as he races down
the hill?
∆v
∆t
6m/s − 1m/s
=
5s
5m/s
=
5s
1m/s
=
1s
= 1m/s2
acceleration =
In words, this means that for each second the cyclist travels downhill, his velocity (in this case, his speed) increases
by 1 meter per second on average. Note that the answer to this problem is expressed in m/s2 , which is the SI unit for
acceleration.
Q: The cyclist slows down at the end of the race. His velocity changes from 6 m/s to 2 m/s during a period of 4
seconds without any change in direction. What was his average acceleration during these 4 seconds?
A: Use the equation given above for acceleration:
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Concept 1. Calculating Acceleration from Velocity and Time
FIGURE 1.1
∆v
∆t
6m/s − 2m/s
=
4s
4m/s
=
4s
1m/s
=
1s
= 1m/s2
acceleration =
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Summary
• To calculate average acceleration when direction is not changing, divide the change in velocity by the change
in time using the formula:
acceleration =
∆v
∆t
• The SI unit for acceleration is m/s2 .
Vocabulary
• acceleration: Measure of the change in velocity of a moving object.
Practice
Practice calculating acceleration by doing the worksheet at this URL:
http://bmuise.wikispaces.com/file/view/Acceleration+Worksheet+4.pdf
Review
1. Write the equation for acceleration without a change in direction.
2. What is the SI unit for acceleration?
3. During the final 5 seconds of a race, a cyclist increased her velocity from 4 m/s to 7 m/s. What was her average
acceleration during those last 5 seconds?
References
1. . . Used under license from Shutterstock.com
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