Kinematics Average Acceleration. Variables In addition to the variables previously used to calculate...
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Kinematics Average Acceleration
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Transcript of Kinematics Average Acceleration. Variables In addition to the variables previously used to calculate...
Kinematics
Average Acceleration
Variables
• In addition to the variables previously used to calculate average velocity (vavg), we add one more:
• a- acceleration (m/s2)aavg- average acceleration
Solving for acceleration
• Acceleration can be found 2 ways:
• Graphically- read from a Velocity vs. Time graph
• Mathematically- found using an equation
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)
Graphically
• The slope is Δv/Δt = (10m/s) / (5s)
• Look at the UNITS of the slope…
0 1 2 3 4 5 60
2
4
6
8
10
12
Velocity vs. Time
Time (s)
Velci
ty (m
/s)
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
Same units as
acceleration.
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.
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
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.
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=?
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
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
Practice
• Page 49, Practice B.
• ALL units will be in meters, seconds, and m/s.
