Chapter 6A. Acceleration

1. Chapter 6A. Acceleration A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

3. Objectives: After completing this module, you should be able to: Define and apply concepts of average and instantaneous velocity and acceleration. Solve problems involving initial and final velocity, acceleration, displacement, and time. Demonstrate your understanding of directions and signs for velocity, displacement, and acceleration. Solve problems involving a free-falling body in a gravitational field.

4. Uniform Acceleration in One Dimension: Motion is along a straight line (horizontal, vertical or slanted). Changes in motion result from a CONSTANT force producing uniform acceleration. The cause of motion will be discussed later. Here we only treat the changes. The moving object is treated as though it were a point particle.

5. Distance and Displacement Distance is the length of the actual path taken by an object. Consider travel from point A to point B in diagram below:

6. Distance and Displacement Displacement is the straight-line separation of two points in a specified direction.

7. Distance and Displacement For motion along x or y axis, the displacement is determined by the x or y coordinate of its final position. Example: Consider a car that travels 8 m, E then 12 m, W.

8. The Signs of Displacement Displacement is positive (+) or negative (-) based on LOCATION.

9. Definition of Speed Speed is the distance traveled per unit of time (a scalar quantity).

10. Definition of Velocity Velocity is the displacement per unit of time. (A vector quantity.)

11. Example 1. A runner runs 200 m, east, then changes direction and runs 300 m, west. If the entire trip takes 60 s, what is the average speed and what is the average velocity?

12. Example 1 (Cont.) Now we find the average velocity, which is the net displacement divided by time. In this case, the direction matters.

13. Example 2. A sky diver jumps and falls for 600 m in 14 s. After chute opens, he falls another 400 m in 150 s. What is average speed for entire fall?

14. Examples of Speed

15. Speed Examples (Cont.)

16. Average Speed and Instantaneous Velocity

17. The Signs of Velocity

18. Average and Instantaneous v

19. Definition of Acceleration

20. Acceleration and Force

21. Example of Acceleration

22. The Signs of Acceleration Acceleration is positive (+) or negative (-) based on the direction of force.

23. Average and Instantaneous a

24. Example 3 (No change in direction): A constant force changes the speed of a car from 8 m/s to 20 m/s in 4 s. What is average acceleration?

25. Example 3 (Continued): What is average acceleration of car?

26. Example 4: A wagon moving east at 20 m/s encounters a very strong head-wind, causing it to change directions. After 5 s, it is traveling west at 5 m/s. What is the average acceleration? (Be careful of signs.)

27. Example 4 (Cont.): Wagon moving east at 20 m/s encounters a head-wind, causing it to change directions. Five seconds later, it is traveling west at 5 m/s. What is the average acceleration?

32. Definitions

33. Velocity for constant a

34. Example 5: A ball 5 m from the bottom of an incline is traveling initially at 8 m/s. Four seconds later, it is traveling down the incline at 2 m/s. How far is it from the bottom at that instant?

36. Constant Acceleration

37. Acceleration in our Example

38. Formulas based on definitions:

39. Use of Initial Position x0 in Problems.

40. Review of Symbols and Units Displacement (x, xo); meters (m) Velocity (v, vo); meters per second (m/s) Acceleration (a); meters per s2 (m/s2) Time (t); seconds (s)

41. The Signs of Displacement Displacement is positive (+) or negative (-) based on LOCATION.

42. The Signs of Velocity Velocity is positive (+) or negative (-) based on direction of motion.

43. Acceleration Produced by Force Acceleration is (+) or (-) based on direction of force (NOT based on v).

44. Problem Solving Strategy: Draw and label sketch of problem. Indicate + direction and force direction. List givens and state what is to be found.

45. Example 6: A airplane flying initially at 400 ft/s lands on a carrier deck and stops in a distance of 300 ft. What is the acceleration?

46. Example: (Cont.)

48. Acceleration Due to Gravity Every object on the earth experiences a common force: the force due to gravity. This force is always directed toward the center of the earth (downward). The acceleration due to gravity is relatively constant near the Earth�s surface.

49. Gravitational Acceleration In a vacuum, all objects fall with same acceleration. Equations for constant acceleration apply as usual. Near the Earth�s surface:

50. Experimental Determination of Gravitational Acceleration.

51. Experimental Determination of Gravity (y0 = 0; y = -1.20 m)

52. Sign Convention: A Ball Thrown Vertically Upward

53. Same Problem Solving Strategy Except a = g: Draw and label sketch of problem. Indicate + direction and force direction. List givens and state what is to be found.

54. Example 7: A ball is thrown vertically upward with an initial velocity of 30 m/s. What are its position and velocity after 2 s, 4 s, and 7 s?

55. Finding Displacement:

56. Finding Velocity:

57. Example 7: (Cont.) Now find the maximum height attained:

58. Example 7: (Cont.) Finding the maximum height:

59. Summary of Formulas

60. Summary: Procedure

61. CONCLUSION OF Chapter 6 - Acceleration