Introduction to Motion

1. Introduction to Motion Position-Time Graphs Velocity-Time Graphs Acceleration-Time Graphs

2. First, Let’s define some important terms: • Position • Distance • Displacement • Speed • Average velocity • Instantaneous velocity • Average Acceleration • Instantaneous Acceleration

3. r = 1 m Position: Where it is. Distance: path length in meters; a scalar Displacement: final position minus initial position, in meters. Displacement is a VECTOR! distance = 2p m Dx= 0 m

4. One revolution in 3.14 s. r = 1 m Speed: distance divided by total time, in m/s Average velocity: displacement divided by total time, in m/s. Velocity is a VECTOR! speed = 2 m/s vav = 0 m/s

5. A horse canters away from its trainer in a straight line, • moving 150 m away in 14 s. It then turns abruptly and • gallops halfway back in 4.5 s. Calculate • its average speed for the entire trip and • its average velocity for the entire trip. • Use “away from the trainer” as the positive direction.

6. x (m) t (s) • Instantaneous velocity: velocity at one point in time, in m/s. • It is a VECTOR!

7. Average Acceleration: rate of change of velocity, in m/s2. • It is a VECTOR! • Instantaneous Acceleration: acceleration at one point in time, in m/s2. • Also a VECTOR!

8. Graph things every physics student should know: Initial position, x0 velocity Nothing Initial velocity, v0 acceleration Displacement Initial acceleration, a0 Change in Velocity Jerk

9. x t WALK THIS WAY:

10. x t WALK THIS WAY:

11. x t WALK THIS WAY:

12. x t WALK THIS WAY:

13. x t WALK THIS WAY: Y-intercept? Slope?

14. v t WALK THIS WAY (NOTE - VELOCITY GRAPH):

15. v t WALK THIS WAY (NOTE - VELOCITY GRAPH):

16. v t WALK THIS WAY (NOTE - VELOCITY GRAPH): Y-intercept? Slope? Area under curve?

17. a t WALK THIS WAY (NOTE – ACCELERATION GRAPH):

18. a t WALK THIS WAY (NOTE – ACCELERATION GRAPH): Y-intercept? Area under curve? Slope?

19. v (m/s) 25 20 15 10 5 t (s) 0 10 15 20 5 Draw the corresponding acceleration-time graph: Draw the corresponding position-time graph.

20. Summarize! Review your notes for three minutes and mark the key ideas from the discussion. Then, trade with a partner to see if you have marked the same things.

21. Graph things every physics student should know: Initial position, x0 velocity Nothing Initial velocity, v0 acceleration Displacement Initial acceleration, a0 Change in Velocity Jerk

22. Notation • Delta, D • Subscripts • i, 0 • f • 0, I, 2

23. Common word problem phrases Starts from rest…v0=0 ...after __ sec… Dt=___ Comes to rest, vf=0 Initial…at time =0 Moves a total of _ meters…Dx=__ …max height…v @ hmax=0, and Dh=