Chapter 2. Kinematics in One Dimension

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.

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.

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.

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.

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.

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.

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.

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.

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 Δtcontinues 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 Δtapproaches 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