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.

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 v A B vv t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 seconds? What can you conclude about the object’s motion from seconds? Velocity vs. Time Graphs

What can you conclude about these objects’ motions?

Draw representative graphs for a particle which is stationary. x t Position vs time v t Velocity vs time a t Acceleration vs time

Draw representative graphs for a particle which has constant non-zero velocity. x t Position vs time v t Velocity vs time a t Acceleration vs time

x t Position vs time v t Velocity vs time a t Acceleration vs 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 seconds. Velocity vs. Time Graphs

Find the displacement from 0 s to 4.0 s v (m/s) 2.0 t (s)