1. Linear Motion III Acceleration, Velocity vs. Time Graphs

2. 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.

3. Example: Listen to the song, “In a Hurry” and calculate the average acceleration of the car mentioned in the lyrics.

4. 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?

5. Average Acceleration from a Graph t v A B vv tt

6. 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

7. 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

8. 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

9. 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

10. What can you conclude about these objects’ motions?

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

12. 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

13. 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.

14. 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

15. 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

16. 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

17. 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

18. Determine the change in position of the particle from 0-6 seconds. Velocity vs. Time Graphs

19. Displacement = Area under/over curve Finding Displacement from Velocity vs. Time Graphs

20. Determine the change in position of the particle from 6-9 seconds. Velocity vs. Time Graphs

21. Determine the change in position of the particle from 12-13 seconds. Velocity vs. Time Graphs

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