1. KinematicsKinematics - The branch of classical mechanics that describes the motions of points, bodies (objects) and systems of bodies (groups of objects) without consideration of the causes of motion. Mechanics Lecture 1, Slide 1 Kinematics

2. Classical Mechanics Lecture 1 Today's Concepts: a) Displacement, Velocity, Acceleration b) 1-D Kinematics with constant acceleration Mechanics Lecture 1, Slide 2 If you haven't done Prelecture 1 yet, please do so later today

3. Pre-lecture Viewing Times Mechanics Lecture 1, Slide 3 Slide 1: 1.10 min Slide 2: 2.27 min Slide 3: 1.98 min Slide 4: 1.83 min Slide 5: 2.03 min Slide 6: question Slide 7: 2.17 min Slide 8: 2.12 min Slide 9: question Slide 10: 1.85 min Slide 11: 0.87 min Minimum Total Viewing time = 16.2 minutes Good!???!

4. Mechanics Lecture 1, Slide 4 Lecture Thoughts

5. Main Points of Unit 1 Mechanics Lecture 1, Slide 5

6. Main Points of Unit 1 Mechanics Lecture 1, Slide 6

7. Mechanics Lecture 1, Slide 7 Prelecture Example Displacement

8. Mechanics Lecture 1, Slide 8 Prelecture Example Displacement

9. Mechanics Lecture 1, Slide 9 Displacement Time taken Displacement and Velocity in One Dimension But what about ?

10. Mechanics Lecture 1, Slide 10 Definition: Speed = |v(t)| The v(t) vs. t plot is just the slope of the x(t) vs. t plot Displacement and Velocity in One Dimension The slope of the x(t) vs. t plot is the “derivative” of x(t) w.r.t t. Limit of  t  0

11. Mechanics Lecture 1, Slide 11 Displacement and Velocity in One Dimension

12. The Derivative Mechanics Lecture 1, Slide 12

13. The Derivative Mechanics Lecture 1, Slide 13 BUILD FROM HERE…

14. Mechanics Lecture 1, Slide 14 Displacement as a function of velocity

15. The Definite Integral Mechanics Lecture 1, Slide 15

16. The Definite Integral Mechanics Lecture 1, Slide 16

17. The Definite Integral Mechanics Lecture 1, Slide 17 Integral : “Anti-derivative”

18. Displacement and Velocity in one dimension A. Yes B. NO Mechanics Lecture 1, Slide 18 Are the plots shown at the left correctly related?

19. Prelecture Question 1 Mechanics Lecture 1, Slide 19

20. Prelecture Question 1 Mechanics Lecture 1, Slide 20

21. Prelecture Help Question 1 Mechanics Lecture 1, Slide 21

22. Mechanics Lecture 1, Slide 22 For the Displacement and Velocity curves shown on the left, which is the correct plot of acceleration vs. time? A B Checkpoint 1

23. Mechanics Lecture 1, Slide 23 A B Correct answer Checkpoint 1

24. Mechanics Lecture 1, Slide 24 Checkpoint 1-responses

25. Mechanics Lecture 1, Slide 25 Checkpoint 1-responses

26. Mechanics Lecture 1, Slide 26 The velocity vs. time plot of some object is shown to the right. Which diagram below could be the Displacement vs. time plot for the same object? ABC Clicker Question

27. Which Plot? A. Plot A B. Plot B C. Plot C D. None of the above Mechanics Lecture 1, Slide 27 ABC

28. Mechanics Lecture 1, Slide 28 The velocity vs. time plot of some object is shown to the right. Which diagram below could be the Displacement vs. time plot for the same object? ABC Clicker Question

29. Mechanics Lecture 1, Slide 29 Acceleration

30. Velocity,Acceleration Signed quantity Mechanics Lecture 1, Slide 30

31. Velocity,Acceleration Signed quantity Mechanics Lecture 1, Slide 31 negative acceleration Car slowing down while moving in + direction a<0 Car slowing down while moving in - direction a>0

32. Prelecture Question 2 Mechanics Lecture 1, Slide 32

33. Prelecture Question 2 Mechanics Lecture 1, Slide 33

34. Motion with Constant Acceleration Mechanics Lecture 1, Slide 34

35. Motion with Constant Acceleration Velocity vs displacement Mechanics Lecture 1, Slide 35 Let’s eliminate time…to obtain v(x) for special case of constant acceleration

36. Mechanics Lecture 1, Slide 36 Motion with Constant Acceleration constant a(t) = a

37. Mechanics Lecture 1, Slide 37 At t = 0 a ball, initially at rest, starts to roll down a ramp with constant acceleration. Suppose it moves 1 foot between t = 0 sec and t = 1 sec. How far does it move between t = 1 sec and t = 2 sec ? A) 1 foot B) 2 feet C) 3 feet D) 4 feet E) 6 feet Checkpoint 2

38. Mechanics Lecture 1, Slide 38 1ft 4ft 9ft ? 16ft At t = 0 a ball, initially at rest, starts to roll down a ramp with constant acceleration. Suppose it moves 1 foot between t = 0 sec and t = 1 sec. How far does it move between t = 1 sec and t = 2 sec ? A) 1 foot B) 2 feet C) 3 feet D) 4 feet E) 6 feet Checkpoint 2

39. Mechanics Lecture 1, Slide 39 Checkpoint 2 Responses

40. Mechanics Lecture 1, Slide 40 Checkpoint 2 Responses

41. Mechanics Lecture 1, Slide 41 1ft 4ft 9 ft 3 16f t Checkpoint 2 Solution

42. Summary Mechanics Lecture 1, Slide 42

43. Summary Mechanics Lecture 1, Slide 43 Direct Relationship between velocity and displacement (time dependence removed) for special case of constant acceleration

44. Acceleration Mechanics Lecture 1, Slide 44 https://www.smhttps://www.smartphysics.com/Course/PlaySlideshow?unitItemID=192801&enrollmentID=29042artphysics.com/Course/PlaySlideshow?unitIte mID=192801&enrollmentID=29042

45. Schaum’s Outline Mechanics Lecture 1, Slide 45

46. Displacement,Velocity & Acceleration Mechanics Lecture 1, Slide 46 Need to become comfortable with displacement, velocity and acceleration and how they are related!!!

47. Constant Acceleration Mechanics Lecture 1, Slide 47

48. Mechanics Lecture 1, Slide 48

49. Hyperphysics-Motion Mechanics Lecture 1, Slide 49 http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html

50. Hyperphysics-Motion Mechanics Lecture 1, Slide 50 http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html

51. Hyperphysics Motion Mechanics Lecture 1, Slide 51 Displacement vs timet Velocity vs timet Acceleration vs timet

52. Hyperphysics Motion Mechanics Lecture 1, Slide 52

53. Main Points of Unit 1 Mechanics Lecture 1, Slide 53

54. Main Points of Unit 1 Mechanics Lecture 1, Slide 54

55. A “real world” ramp experiment Mechanics Lecture 1, Slide 55 Kilometre lance http://www.kl-france.com/http://www.kl-france.com/

56. A “real world” ramp experiment Mechanics Lecture 1, Slide 56 Could not find elapsed times…to check. Assume constant acceleration Verbier- Mont Fort