kinematics
DESCRIPTION
Kinematics. Average Acceleration. Variables. In addition to the variables previously used to calculate average velocity ( v avg ), we add one more: a- acceleration (m/s 2 ) a avg - average acceleration. Solving for acceleration. Acceleration can be found 2 ways: - PowerPoint PPT PresentationTRANSCRIPT
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*
25/10 sm
ssm
ssm
tv
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*
25/10 sm
ssm
ssm
tv
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.
tvv
tva if
avg
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: tvv
a 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:
ssmsmt
smtsmt
smsmsm
tvv
a 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.