1. Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous

2. Uniform motion  d = 60 cm  t = 15 sec  d = 60 cm  t = 15 sec

3. Interpret: 60/15 = 4 cm/sec  d = 60 cm  t = 15 sec

4. Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous

5. Graphing uniform motion  d = 60 cm  t = 15 sec

6. A graph is a collection of points Time (sec) Position (cm) 5 10 15 202530 60 120 0 0

7. Uniform motion

8. A graph is a collection of points Time (sec) 5 10 15 202530 60 120 0 0 Position (cm)

9. Uniform motion  d = 60 cm  t = 15 sec

10. A graph is a collection of points Time (sec) 5 10 15 202530 60 120 0 0 Position (cm)

11. A graph is a collection of points Time (sec) 5 10 15 202530 60 120 0 0 Position (cm)

12. Uniform motion  d = 60 cm  t = 15 sec

13. A graph is a collection of points Time (sec) 5 10 15 202530 60 120 0 0 Position (cm)

14. A graph is a collection of points Time (sec) 5 10 15 202530 60 120 0 0 Position (cm)

15. A graph is a collection of points Time (sec) 5 10 15 202530 60 120 0 0 Position (cm)

16. How do we find the velocity? Time (sec) 5 10 15 202530 60 120 0 0 rise  d run  t slope = rise run = dd tt velocity = =4 cm/s Position (cm) 40 100 = 60 cm = 15 s

17. Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous

18. Average velocity Left home at 5:00pm At 6:00pm I was 60 miles from home What was my velocity at 5:30pm?

19. Operational definition of average velocity dd tt v ave =

20. Interpretation of average velocity Start Finish The hare’s average velocity is the uniform velocity of the tortoise. In other words, how fast would the tortoise have to plod along to start and finish the race at the same time as the hare?

21. Interpretation of average velocity Start Finish Problem: If the hare traveled at a uniform 10 miles/hour for the first hour and a uniform 4 miles/hour for the last two hours, what was the hare’s average velocity? What was the tortoise’s uniform velocity?

22. Does this bullet have a velocity at the instant shown? picture courtesy of the late, great Doc Edgerton

23. Velocity Operational definition: dd tt v= Three flavors of velocity uniform average instantaneous

24. What is the velocity of this truck?  t = 4 sec

25. What is the velocity at t = 2 sec? rise  d run  t slope = rise run = dd tt instantaneous velocity = Position (m)

26. Why use the tangent line? Position (m)

27. Let’s take a closer look Position (m)

28. Let’s take a closer look Position (m)

29. Perhaps even closer Position (m)

30. This is close enough The slope of this line is 4 m/s What interpretation can we give to this slope? Position (m)

31. Now extend this line in both directions and it becomes the tangent Position (m)

32. Now extend this line in both directions and it becomes the tangent Position (m)

33. Instantaneous velocity Position (m)

34. Consider the following statement: “  d/  t gives the velocity for an interval. If we want the velocity at just one instant, we would divide the position at that instant by the time at that instant: v = d/t.” Is this right? It’s 12 noon and I’m in Silver Bay.....how fast am I going?

35. How do you move a pencil to create the following graph? time position

36. What is the corresponding velocity versus time graph? time velocity

37. How do you move a pencil to create the following graph? time position

38. What is the corresponding velocity versus time graph? time velocity

39. How do you move a pencil to create the following graph? time position

40. What is the corresponding velocity versus time graph? time velocity

41. Slope = ? time position

42. Slope = ? time position

43. What’s the velocity at t=0?

44. Graphing velocity Time (sec) Velocity (m/s) 1 2 3 45 6 2 4 0 0 6 8

45. What’s the velocity at t=1?

46. Graphing velocity Time (sec) 1 2 3 45 6 2 4 0 0 6 8 Velocity (m/s)

47. What’s the velocity at t=3?

48. Graphing velocity Time (sec) 1 2 3 45 6 2 4 0 0 6 8 Velocity (m/s)

49. What’s the velocity at t=4?

50. Graphing velocity Time (sec) 1 2 3 45 6 2 4 0 0 6 8 Velocity (m/s)

51. Graphing velocity Time (sec) 1 2 3 45 6 2 4 0 0 6 8 Velocity (m/s)

52. How do you move a pencil to create the following graph? time velocity

53. How do you move a pencil to create the following graph? time velocity +5 -5 0

54. Velocity Read Chapter 2