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Linear Motion III
Acceleration, Velocity vs. Time Graphs
Average Acceleration
Average acceleration describes how fast (the rate) the velocity is changing with respect to time. The equation is:
Acceleration is a vector quantity because it includes magnitude and direction.
ave
xv t
at t
Example: Listen to the song, “In a Hurry” and calculate the average acceleration of the car mentioned in the lyrics.
Example: It takes a motorist half a minute to change his speed from 10 m/s to 40 m/s. What is his average acceleration?
Average Acceleration from a Graph
t
vA
B
v
t
ave
va
t
Average and Instantaneous Acceleration
t
v
Average acceleration is represented by the slope of a line connecting two points on a v/t graph.
Instantaneous acceleration is represented by the slope of a tangent to the curve on a v/t graph.
A
B
C
What can you conclude about the object’s motion from 0-6 seconds? Notice that the tangent line at every instant during this interval is the same.
What is the object’s acceleration from 0-6 seconds?
Velocity vs. Time Graphs
What is the object’s acceleration from 6-9 seconds?
What can you conclude about the object’s motion from 6-9 seconds?
Velocity vs. Time Graphs
What is the object’s acceleration from 14-15 seconds?
What can you conclude about the object’s motion from 14-15 seconds?
Velocity vs. Time Graphs
Velocity vs. Time GraphsWhat can you conclude about these objects’ motions?
Draw representative graphs for a particle which is stationary.
x
t
Positionvs
time
v
t
Velocityvs
time
a
t
Accelerationvs
time
Draw representative graphs for a particle which has constant non-zero velocity.
x
t
Positionvs
time
v
t
Velocityvs
time
a
t
Accelerationvs
time
x
t
Positionvs
time
v
t
Velocityvs
time
a
t
Accelerationvs
time
Draw representative graphs for a particle which has constant non-zero acceleration.
Sample problem: Consider an object that is dropped from rest and reaches terminal velocity during its fall. What would the x vs t graph look like?
t
x
Sample problem: Consider an object that is dropped from rest and reaches terminal velocity during its fall. What would the v vs t graph look like?
t
v
Sample problem: A ball is thrown straight up and then falls straight back down and is caught a few seconds later. What would the x vs t graph look like?
t
x
Sample problem: A ball is thrown straight up and then falls straight back down and is caught a few seconds later. What would the v vs t graph look like?
t
v
Determine the change in position of the particle from 0-6 seconds.
Velocity vs. Time Graphs
Displacement = Area under/over curve
Finding Displacement from Velocity vs. Time Graphs
Determine the change in position of the particle from 6-9 seconds.
Velocity vs. Time Graphs
Determine the change in position of the particle from 12-13 seconds.
Velocity vs. Time Graphs
Find the displacement from 0 s to 4.0 s
v (m/s)
2.0
t (s)2.0 4.0
