1. Chapter 2. Kinematics in One Dimension
In this chapter we study kinematics of motion in one dimension—motion along a straight line. Runners, drag racers, and skiers are just a few examples of motion in one dimension.
Chapter Goal: To learn how to solve problems about motion in a straight line.

2. Chapter 2. Kinematics in One Dimension
Topics:
Uniform Motion
Instantaneous Velocity
Finding Position from Velocity
Motion with Constant Acceleration
Free Fall
Motion on an Inclined Plane
Instantaneous Acceleration

3. Chapter 2. Reading Quizzes

4. The slope at a point on a position- versus-time graph of an object is
the object’s speed at that point.
the object’s average velocity at that point.
the object’s instantaneous velocity at that point.
the object’s acceleration at that point.
the distance traveled by the object to that point.
Answer: C

5. The slope at a point on a position- versus-time graph of an object is
the object’s speed at that point.
the object’s average velocity at that point.
the object’s instantaneous velocity at that point.
the object’s acceleration at that point.
the distance traveled by the object to that point.
IG2.1

6. The area under a velocity-versus-time graph of an object is
the object’s speed at that point.
the object’s acceleration at that point.
the distance traveled by the object.
the displacement of the object.
This topic was not covered in this chapter.
Answer: D

7. The area under a velocity-versus-time graph of an object is
the object’s speed at that point.
the object’s acceleration at that point.
the distance traveled by the object.
the displacement of the object.
This topic was not covered in this chapter.
IG2.2

8. At the turning point of an object,
the instantaneous velocity is zero.
the acceleration is zero.
both A and B are true.
neither A nor B is true.
This topic was not covered in this chapter.
Answer: A

9. At the turning point of an object,
the instantaneous velocity is zero.
the acceleration is zero.
both A and B are true.
neither A nor B is true.
This topic was not covered in this chapter.
IG2.3

10. A 1-pound block and a 100-pound block are placed side by side at the top of a frictionless hill. Each is given a very light tap to begin their race to the bottom of the hill. In the absence of air resistance
the 1-pound block wins the race.
the 100-pound block wins the race.
the two blocks end in a tie.
there’s not enough information to determine which block wins the race.
Answer: C

11. A 1-pound block and a 100-pound block are placed side by side at the top of a frictionless hill. Each is given a very light tap to begin their race to the bottom of the hill. In the absence of air resistance
the 1-pound block wins the race.
the 100-pound block wins the race.
the two blocks end in a tie.
there’s not enough information to determine which block wins the race.
IG2.4

12. Chapter 2. Basic Content and Examples

13. Uniform Motion
Straight-line motion in which equal displacements occur during any successive equal-time intervals is called uniform motion. For one-dimensional motion, average velocity is given by

14. EXAMPLE 2.1 Skating with constant velocity

15. EXAMPLE 2.1 Skating with constant velocity

16. EXAMPLE 2.1 Skating with constant velocity

17. EXAMPLE 2.1 Skating with constant velocity

18. EXAMPLE 2.1 Skating with constant velocity

19. EXAMPLE 2.1 Skating with constant velocity

20. Tactics: Interpreting position-versus-time graphs

21. Tactics: Interpreting position-versus-time graphs

22. Instantaneous Velocity
Average velocity becomes a better and better approximation to the instantaneous velocity as the time interval over which the average is taken gets smaller and smaller.
As Δt continues to get smaller, the average velocity vavg = Δs/Δt reaches a constant or limiting value. That is, the instantaneous velocity at time t is the average velocity during a time interval Δt centered on t, as Δt approaches zero.

23. EXAMPLE 2.4 Finding velocity from position graphically
QUESTION:

24. EXAMPLE 2.4 Finding velocity from position graphically

25. EXAMPLE 2.4 Finding velocity from position graphically

26. EXAMPLE 2.4 Finding velocity from position graphically

27. EXAMPLE 2.4 Finding velocity from position graphically

28. EXAMPLE 2.4 Finding velocity from position graphically

29. Finding Position from Velocity
If we know the initial position, si, and the instantaneous velocity, vs, as a function of time, t, then the final position is given by
Or, graphically;

30. EXAMPLE 2.7 The displacement during a drag race
QUESTION:

31. EXAMPLE 2.7 The displacement during a drag race

32. EXAMPLE 2.7 The displacement during a drag race

33. EXAMPLE 2.7 The displacement during a drag race

34. Motion with Constant Acceleration

37. Problem-Solving Strategy: Kinematics with constant acceleration

38. Problem-Solving Strategy: Kinematics with constant acceleration

39. Problem-Solving Strategy: Kinematics with constant acceleration

40. Problem-Solving Strategy: Kinematics with constant acceleration

41. EXAMPLE 2.14 Friday night football
QUESTION:

42. EXAMPLE 2.14 Friday night football

43. EXAMPLE 2.14 Friday night football

44. EXAMPLE 2.14 Friday night football

45. EXAMPLE 2.14 Friday night football

46. EXAMPLE 2.14 Friday night football

47. EXAMPLE 2.14 Friday night football

48. Motion on an Inclined Plane

49. EXAMPLE 2.17 Skiing down an incline
QUESTION:

50. EXAMPLE 2.17 Skiing down an incline

51. EXAMPLE 2.17 Skiing down an incline

52. EXAMPLE 2.17 Skiing down an incline

53. EXAMPLE 2.17 Skiing down an incline

54. Tactics: Interpreting graphical representations of motion

55. Instantaneous Acceleration
The instantaneous acceleration as at a specific instant of time t is given by the derivative of the velocity

56. Finding Velocity from the Acceleration
If we know the initial velocity, vis, and the instantaneous acceleration, as, as a function of time, t, then the final velocity is given by
Or, graphically,

57. EXAMPLE 2.21 Finding velocity from acceleration
QUESTION:

58. EXAMPLE 2.21 Finding velocity from acceleration

59. Chapter 2. Summary Slides

60. General Principles

61. General Principles

62. Important Concepts

63. Important Concepts

64. Applications

65. Applications

66. Chapter 2. Clicker Questions

67. Which position-versus-time graph represents the motion shown in the motion diagram?
Answer: D

68. Which position-versus-time graph represents the motion shown in the motion diagram?
STT2.1

69. Which velocity-versus-time graph goes with the position-versus-time graph on the left?
Answer: C

70. Which velocity-versus-time graph goes with the position-versus-time graph on the left?
STT2.2

71. Which position-versus-time graph goes with the velocity-versus-time graph at the top? The particle’s position at ti = 0 s is xi = –10 m.
Answer: B

72. Which position-versus-time graph goes with the velocity-versus-time graph at the top? The particle’s position at ti = 0 s is xi = –10 m.
STT2.3

73. Which velocity-versus-time graph or graphs goes with this acceleration-versus- time graph? The particle is initially moving to the right and eventually to the left.
Answer: B

74. Which velocity-versus-time graph or graphs goes with this acceleration-versus- time graph? The particle is initially moving to the right and eventually to the left.
STT2.4

75. The ball rolls up the ramp, then back down
The ball rolls up the ramp, then back down. Which is the correct acceleration graph?
Answer: D

76. The ball rolls up the ramp, then back down
The ball rolls up the ramp, then back down. Which is the correct acceleration graph?
STT2.5

77. Rank in order, from largest to smallest, the accelerations aA– aC at points A – C.
aA > aB > aC
aA > aC > aB
aB > aA > aC
aC > aA > aB
aC > aB > aA
Answer: E

78. Rank in order, from largest to smallest, the accelerations aA– aC at points A – C.
aA > aB > aC
aA > aC > aB
aB > aA > aC
aC > aA > aB
aC > aB > aA
STT2.6