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