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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. In this chapter we study kinematics of motion in one dimensionmotion along.

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Presentation on theme: "Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. In this chapter we study kinematics of motion in one dimensionmotion along."— Presentation transcript:

1 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. In this chapter we study kinematics of motion in one dimensionmotion 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. Chapter 2. Kinematics in One Dimension

2 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Topics: Uniform Motion Instantaneous Velocity Finding Position from Velocity Motion with Constant Acceleration Free Fall Motion on an Inclined Plane Instantaneous Acceleration Chapter 2. Kinematics in One Dimension

3 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 2. Reading Quizzes

4 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The slope at a point on a position- versus-time graph of an object is A. the objects speed at that point. B. the objects average velocity at that point. C. the objects instantaneous velocity at that point. D. the objects acceleration at that point. E. the distance traveled by the object to that point.

5 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The slope at a point on a position- versus-time graph of an object is A. the objects speed at that point. B. the objects average velocity at that point. C. the objects instantaneous velocity at that point. D. the objects acceleration at that point. E. the distance traveled by the object to that point.

6 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The area under a velocity-versus- time graph of an object is A. the objects speed at that point. B. the objects acceleration at that point. C. the distance traveled by the object. D. the displacement of the object. E. This topic was not covered in this chapter.

7 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The area under a velocity-versus- time graph of an object is A. the objects speed at that point. B. the objects acceleration at that point. C. the distance traveled by the object. D. the displacement of the object. E. This topic was not covered in this chapter.

8 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. At the turning point of an object, A. the instantaneous velocity is zero. B. the acceleration is zero. C. both A and B are true. D. neither A nor B is true. E. This topic was not covered in this chapter.

9 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. At the turning point of an object, A. the instantaneous velocity is zero. B. the acceleration is zero. C. both A and B are true. D. neither A nor B is true. E. This topic was not covered in this chapter.

10 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 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 A. the 1-pound block wins the race. B. the 100-pound block wins the race. C. the two blocks end in a tie. D. theres not enough information to determine which block wins the race.

11 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 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 A. the 1-pound block wins the race. B. the 100-pound block wins the race. C. the two blocks end in a tie. D. theres not enough information to determine which block wins the race.

12 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 2. Basic Content and Examples

13 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 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 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.1 Skating with constant velocity

15 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.1 Skating with constant velocity

16 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.1 Skating with constant velocity

17 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.1 Skating with constant velocity

18 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.1 Skating with constant velocity

19 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.1 Skating with constant velocity

20 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Tactics: Interpreting position-versus-time graphs

21 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Tactics: Interpreting position-versus-time graphs

22 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 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 v avg = Δ s/ Δ t reaches a constant or limiting value. That is, the instantaneous velocity at time t is the average velocity during a time interval Δ t centered on t, as Δt approaches zero.

23 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.4 Finding velocity from position graphically QUESTION:

24 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.4 Finding velocity from position graphically

25 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.4 Finding velocity from position graphically

26 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.4 Finding velocity from position graphically

27 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.4 Finding velocity from position graphically

28 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.4 Finding velocity from position graphically

29 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Finding Position from Velocity If we know the initial position, s i, and the instantaneous velocity, v s, as a function of time, t, then the final position is given by Or, graphically;

30 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.7 The displacement during a drag race QUESTION:

31 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.7 The displacement during a drag race

32 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.7 The displacement during a drag race

33 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.7 The displacement during a drag race

34 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Motion with Constant Acceleration

35 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

36

37 Problem-Solving Strategy: Kinematics with constant acceleration

38 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Problem-Solving Strategy: Kinematics with constant acceleration

39 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Problem-Solving Strategy: Kinematics with constant acceleration

40 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Problem-Solving Strategy: Kinematics with constant acceleration

41 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.14 Friday night football QUESTION:

42 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.14 Friday night football

43 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.14 Friday night football

44 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.14 Friday night football

45 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.14 Friday night football

46 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.14 Friday night football

47 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.14 Friday night football

48 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Motion on an Inclined Plane

49 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.17 Skiing down an incline QUESTION:

50 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.17 Skiing down an incline

51 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.17 Skiing down an incline

52 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.17 Skiing down an incline

53 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.17 Skiing down an incline

54 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Tactics: Interpreting graphical representations of motion

55 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Instantaneous Acceleration The instantaneous acceleration a s at a specific instant of time t is given by the derivative of the velocity

56 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Finding Velocity from the Acceleration If we know the initial velocity, v is, and the instantaneous acceleration, a s, as a function of time, t, then the final velocity is given by Or, graphically,

57 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.21 Finding velocity from acceleration QUESTION:

58 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 2.21 Finding velocity from acceleration

59 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 2. Summary Slides

60 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. General Principles

61 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. General Principles

62 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Important Concepts

63 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Important Concepts

64 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Applications

65 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Applications

66 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 2. Clicker Questions

67 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which position-versus-time graph represents the motion shown in the motion diagram?

68 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which position-versus-time graph represents the motion shown in the motion diagram?

69 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which velocity-versus-time graph goes with the position-versus-time graph on the left?

70 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which velocity-versus-time graph goes with the position-versus-time graph on the left?

71 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which position-versus-time graph goes with the velocity-versus-time graph at the top? The particles position at t i = 0 s is x i = –10 m.

72 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which position-versus-time graph goes with the velocity-versus-time graph at the top? The particles position at t i = 0 s is x i = –10 m.

73 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 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.

74 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. 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.

75 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The ball rolls up the ramp, then back down. Which is the correct acceleration graph?

76 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The ball rolls up the ramp, then back down. Which is the correct acceleration graph?

77 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Rank in order, from largest to smallest, the accelerations a A – a C at points A – C. A) a A > a B > a C B) a A > a C > a B C) a B > a A > a C D) a C > a A > a B E) a C > a B > a A

78 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A) a A > a B > a C B) a A > a C > a B C) a B > a A > a C D) a C > a A > a B E) a C > a B > a A Rank in order, from largest to smallest, the accelerations a A – a C at points A – C.


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