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Kinematics
Average Acceleration
![Page 2: Kinematics Average Acceleration. Variables In addition to the variables previously used to calculate average velocity (v avg ), we add one more: a- acceleration](https://reader034.vdocument.in/reader034/viewer/2022042717/56649f415503460f94c60758/html5/thumbnails/2.jpg)
Variables
• In addition to the variables previously used to calculate average velocity (vavg), we add one more:
• a- acceleration (m/s2)aavg- average acceleration
![Page 3: Kinematics Average Acceleration. Variables In addition to the variables previously used to calculate average velocity (v avg ), we add one more: a- acceleration](https://reader034.vdocument.in/reader034/viewer/2022042717/56649f415503460f94c60758/html5/thumbnails/3.jpg)
Solving for acceleration
• Acceleration can be found 2 ways:
• Graphically- read from a Velocity vs. Time graph
• Mathematically- found using an equation
![Page 4: Kinematics Average Acceleration. Variables In addition to the variables previously used to calculate average velocity (v avg ), we add one more: a- acceleration](https://reader034.vdocument.in/reader034/viewer/2022042717/56649f415503460f94c60758/html5/thumbnails/4.jpg)
Graphically
• Imagine a velocity vs time graph:
• Consider the SLOPE of this line.
0 1 2 3 4 5 60
2
4
6
8
10
12
Velocity vs. Time
Time (s)
Velci
ty (m
/s)
![Page 5: Kinematics Average Acceleration. Variables In addition to the variables previously used to calculate average velocity (v avg ), we add one more: a- acceleration](https://reader034.vdocument.in/reader034/viewer/2022042717/56649f415503460f94c60758/html5/thumbnails/5.jpg)
Graphically
• The slope is Δv/Δt = (10m/s) / (5s)
• Look at the UNITS of the slope…
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2
4
6
8
10
12
Velocity vs. Time
Time (s)
Velci
ty (m
/s)
![Page 6: Kinematics Average Acceleration. Variables In addition to the variables previously used to calculate average velocity (v avg ), we add one more: a- acceleration](https://reader034.vdocument.in/reader034/viewer/2022042717/56649f415503460f94c60758/html5/thumbnails/6.jpg)
Graphically
0 1 2 3 4 5 60
2
4
6
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10
12
Velocity vs. Time
Time (s)
Velci
ty (m
/s)
2/2*
25
/10sm
ss
m
s
sm
t
v
Same units as
acceleration.
![Page 7: Kinematics Average Acceleration. Variables In addition to the variables previously used to calculate average velocity (v avg ), we add one more: a- acceleration](https://reader034.vdocument.in/reader034/viewer/2022042717/56649f415503460f94c60758/html5/thumbnails/7.jpg)
Graphically
0 1 2 3 4 5 60
2
4
6
8
10
12
Velocity vs. Time
Time (s)
Velci
ty (m
/s)
2/2*
25
/10sm
ss
m
s
sm
t
v
The SLOPE of a VELOCITY vs. TIME graph represents the ACCELERATION of the moving object.
![Page 8: Kinematics Average Acceleration. Variables In addition to the variables previously used to calculate average velocity (v avg ), we add one more: a- acceleration](https://reader034.vdocument.in/reader034/viewer/2022042717/56649f415503460f94c60758/html5/thumbnails/8.jpg)
Mathematically
• Formula:
• The formula looks like the slope of the velocity vs. time graph: That is where it comes from.
t
vv
t
va ifavg
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Example
• A shuttle bus slows down with an average acceleration of -1.8 m/s2. How long does it take the bus to slow from 9.0 m/s to a complete stop.
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Example
• A shuttle bus slows down with an average acceleration of -1.8 m/s2. How long does it take the bus to slow from 9.0 m/s to a complete stop.
• Givens: a= -1.8 m/s2 vi= 9.0 m/s vf= 0 m/s (implied)• Unknown: t=?
![Page 11: Kinematics Average Acceleration. Variables In addition to the variables previously used to calculate average velocity (v avg ), we add one more: a- acceleration](https://reader034.vdocument.in/reader034/viewer/2022042717/56649f415503460f94c60758/html5/thumbnails/11.jpg)
Example
• A shuttle bus slows down with an average acceleration of -1.8 m/s2. How long does it take the bus to slow from 9.0 m/s to a complete stop.
• Givens: a= -1.8 m/s2 vi= 9.0 m/s vf= 0 m/s (implied)• Unknown: t=?
• Formula: t
vva ifavg
![Page 12: Kinematics Average Acceleration. Variables In addition to the variables previously used to calculate average velocity (v avg ), we add one more: a- acceleration](https://reader034.vdocument.in/reader034/viewer/2022042717/56649f415503460f94c60758/html5/thumbnails/12.jpg)
Example
• A shuttle bus slows down with an average acceleration of -1.8 m/s2. How long does it take the bus to slow from 9.0 m/s to a complete stop.
• Givens: a= -1.8 m/s2 vi= 9.0 m/s vf= 0 m/s (implied)• Unknown: t=?
• Formula:
ssm
smt
smtsm
t
smsmsm
t
vva ifavg
5/8.1
/0.9
/0.9)/8.1(
/0.9/0/8.1
2
2
2
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Practice
• Page 49, Practice B.
• ALL units will be in meters, seconds, and m/s.