1. DISPLACEMENT AND VELOCITY Chapter 2-1

2. Objectives Describe motion in terms of frame of reference, displacement, time and velocity. Calculate displacement, velocity and time interval. Interpret position vs. time graphs.

3. Kinematics deals with the concepts that are needed to describe motion. Dynamics deals with the effect that forces have on motion. Together, kinematics and dynamics form the branch of physics known as Mechanics.

4. Describing Motion: this slide is not in your notes! Are these two motions different?

5. 2.1 Displacement As any object moves from one position to another, the length of the straight line drawn from its initial position to the object’s final position is called displacement.displacement Displacement is the change in position of an object. Displacement doesn’t always tell you distance an object moved.  Displacement = final position – initial position  ∆x = x f -x o ∆x = x f -x  Si units – meters (m)

6. 2.1 Displacement Displacement is not always equal to the distance traveled.  Displacement can be positive or negative. If displacement is positive, the object moves to the right. If the displacement is negative, the object moves to the left.

7. 2.1 Displacement

11. 2.2 Speed and Velocity Average speed is the distance traveled divided by the time required to cover the distance. SI units for speed: meters per second (m/s)

12. 2.2 Speed and Velocity Average velocity is the displacement divided by the elapsed time. SI units for velocity: meters per second (m/s)

13. 2.2 Speed and Velocity Velocity gives both direction and magnitude (amount) while speed only gives the magnitude - no direction  Average velocity does not tell you the speed or velocity of the moving object at each moment or instant. Average velocity can be positive or negative depending on direction moved. Time can never be negative!

14. Average Velocity: The slope of a position vs. time graph is called the average velocity.  ‘Should get something similar to this from your lab data’

15. Average Velocity The definition of average velocity holds even if the slope changes. This would be the slope of the line connected the final and initial points.

16. Average Velocity: Steeper slope means a faster moving object.

17. Speed and velocity: Velocity and speed can be used interchangeably in everyday language  In Physics, however, there is a distinction: Speed is a Scalar quantity (numerical value = magnitude only) Velocity is Vector quantity - Describes motion with both direction and a numerical value (magnitude and direction)

18. Constant Velocity Model: Velocity vs. Time Graph With constant velocity, On a graph of velocity vs. time, displacement can be calculated by finding the area under the graph. If the velocity is negative, the displacement calculate will be negative.

19. Constant Velocity Model: Velocity vs. Time Example Use the graph to calculate the displacement of the object:  From 0 s to 3 s  From 3 s to 6 s  From 6 s to 9 s  From 0 s to 9 s

20. Velocity vs. Time Practice Use the graph to calculate the displacement of the object:  From 0 s to 2 s  From 2 s to 4 s  From 4 s to 7 s  From 7 s to 9 s

21. Practice problem example:- The ‘GUESS’ method If Joe rides his bicycle in a straight line for 15 sec with an average velocity of 12.5 m/s south, how far has he ridden? Given: t = 15 sec, v = 12.5m/s Unknown: D = ? Equation and model: v = D/t (kimenatics) Separate the unknown: D= v.t Substitute and solve: D= 12.5m/s x 15s 187.5m Does the answer make sense? Yes!!

22. More practice:- ‘GUESS’ method

23. More Practice Problems 1.What distance will a car traveling 65 km/hr travel in 3.0 hrs? 2.What distance will be traveled if you are going 120km/hr for 30. min? 3.How long will it take to go150 km traveling at 50 km/hr? 4.How long will it take to travel 200 km traveling 100 m/s? 5.If a rocket travels 5600. km in 3.00 hours, what is its speed? 6.A car travels 240 km in 2.0 hrs and a sprinter travels a 100. m in 9.5 s. Which is traveling faster and by how much?

24. CLASS ASSIGNMENT / HOMEWORK I will not accept late work

25. Acceleration Section 3

26. (REVIEW) Displacement for constant acceleration The displacement from time 0 to time t is the area under the velocity graph from 0 to t. Area = ½ b h t (s) v (m/s)

27. (REVIEW) Displacement for constant acceleration If we don’t know v, we can calculate it from a. Area =l w + ½ b h t (s) v (m/s)

28. Instantaneous Velocity – write this under your instantaneous acceleration paragraph The instantaneous velocity indicates how fast the car moves and the direction of motion at each instant of time.

29. Changes in velocity: The direction of acceleration depends on the direction of the motion and on whether the velocity is increasing or decreasing

30. 2.3 Acceleration The notion of acceleration emerges when a change in velocity is combined with the time during which the change occurs. Acceleration is the measure of how fast something speeds up or slows down

31. 2.3 Acceleration DEFINITION OF AVERAGE ACCELERATION SI units for acceleration: (m/s 2 )

32. 2.3 Acceleration Example 3: Acceleration and Increasing Velocity Determine the average acceleration of the plane. G: U: E: (kinematics ) S:

33. 2.3 Acceleration

34. 2.3 Acceleration Example 3: Acceleration and decreasing Velocity Calculate the average acceleration G: U: E: (kinematics ) S:

35. 2.3 Acceleration

36. Graph for speeding up motion – Acceleration describe the following motion Everyday examples of such motion include: Driving a car Throwing a ball Kids sliding at the playground

37. Changes in velocity: Instantaneous acceleration:  Since in some situations, the acceleration of an object can be constant, as a result, it will be the same value at any instant of time.  The plus or minus sign before the number indicates the two possible directions for the acceleration vector when the motion is along a straight line.

38. Interpret The Graph Below: Distance vs. time The graph shows an object which is not moving (at rest).

39. Interpret The Graph Below: Distance vs. Time (constant velocity) : The object is moving at a constant velocity (not changing).

40. Interpret The Graph Below: Distance vs. Time ( constant negative velocity) This object is moving with a constant velocity (negative – object moving in the opposite direction)

41. Interpret The Graph Below: Distance vs. Time (acceleration) The curve in the graph shows that the objects velocity is changing (increasing) as time passes. This is acceleration.

42. Interpret The Graph Below: Distance vs. Time (deceleration) The curve in the graph shows that the objects velocity is decreasing as time passes. The object is decelerating

43. Interpret The Graph Below: Distance vs. Time In the first part of the graph the object is moving with constant velocity. In the second part of the graph the object is at rest (not moving). In the third part the object is again moving with constant velocity in the opposite direction.

44. Interpret The Graph Below:: Velocity vs. Time (constant velocity) The objects velocity does not change as time passes. Constant velocity.

45. Interpret The Graph Below: Velocity vs. Time (constant acceleration) The objects velocity is increasing as time passes – it is accelerating. The straight line shows that it is constant acceleration.

46. Interpret The Graph Below: Velocity vs. Time (constant acceleration - negative) The objects velocity is decreasing as time passes – it is decelerating / slowing down The straight line shows that it is constant deceleration.

47. 2.4 Equations of Kinematics for Constant Acceleration For one dimensional motion it is customary to dispense with the use of boldface symbols overdrawn with arrows for the displacement, velocity, and acceleration vectors. We will, however, continue to convey the directions with a plus or minus sign.

48. 2.4 Equations of Kinematics for Constant Acceleration Let the object be at the origin when the clock starts.

49. 2.4 Equations of Kinematics for Constant Acceleration

51. 1. The drawing shows the position of a rolling ball at one second intervals. Which one of the following phrases best describes the motion of this ball? a) constant position b) constant velocity c) increasing velocity d) constant acceleration e) decreasing velocity REVIEW

52. 2. A police cruiser is parked by the side of the road when a speeding car passes. The cruiser follows the speeding car. Consider the following diagrams where the dots represent the cruiser’s position at 0.5-s intervals. Which diagram(s) are possible representations of the cruiser’s motion? a) A only b) B, D, or E only c) C only d) E only e) A or C only REVIEW

53. 3. Consider the graph the position versus time graph shown. Which curve on the graph best represents a constantly accelerating car? a) A b) B c) C d) D e) None of the curves represent a constantly accelerating car. REVIEW

54. 4. Consider the graph the position versus time graph shown. Which curve on the graph best represents a car that is initially moving in one direction and then reverses directions? a) A b) B c) C d) D e) None of the curves represent a car moving in one direction then reversing its direction. REVIEW

55. 5. A dog is initially walking due east. He stops, noticing a cat behind him. He runs due west and stops when the cat disappears into some bushes. He starts walking due east again. Then, a motorcycle passes him and he runs due east after it. The dog gets tired and stops running. Which of the following graphs correctly represent the position versus time of the dog? REVIEW

56. 5. The graph below represents the speed of a car traveling due east for a portion of its travel along a horizontal road. Which of the following statements concerning this graph is true? a) The car initially increases its speed, but then the speed decreases at a constant rate until the car stops. b) The speed of the car is initially constant, but then it has a variable positive acceleration before it stops. c) The car initially has a positive acceleration, but then it has a variable negative acceleration before it stops. d) The car initially has a positive acceleration, but then it has a variable positive acceleration before it stops. e) No information about the acceleration of the car can be determined from this graph. REVIEW

57. 2.4 Equations of Kinematics for Constant Acceleration Equations of Kinematics for Constant Acceleration

58. 2.4 Equations of Kinematics for Constant Acceleration G: U: E: (kinematics ) S:

59. 2.4 Equations of Kinematics for Constant Acceleration Example 6 Catapulting a Jet Find its displacement.

60. 2.4 Equations of Kinematics for Constant Acceleration G: U: E: (kinematics ) S:

61. Practice 2C A jet plane lands with a speed of 100 m/s and can accelerate uniformly at a maximum rate of -5.0 m/s 2 as it comes to rest. Can this airplane land at an airport where the runway is 0.80 km long?

62. Practice 2C, p. 53 #3 Constant Acceleration

63. CLASS ASSIGNMENT / HOMEWORK I will not accept late work

64. Chapter 2 Section 6: Falling Objects

65. Free Fall acceleration: An object thrown or dropped in the presence of Earth’s gravity experiences a constant acceleration directed toward the center of the earth. This acceleration is called the free- fall acceleration, or the acceleration due to gravity.  Free fall acceleration is the same for all objects, regardless of their mass.

66. Free fall acceleration: The value for free fall acceleration used in this book is:  g = 9.81 m/s 2. In this book, the direction of the free fall acceleration is considered to be negative because the object accelerates toward earth. Negative Positive

67. 2.6 Freely Falling Bodies

68. Free fall acceleration: Since gravity on earth is constant at 9.81m/s 2,  If 2 objects of different masses are dropped from the same height, they will both hit the ground at the same time considering no air resistance. No matter what their masses are. If there is air resistance, some objects may be slowed down The more surface area an object has, the more air resistance it will experience.  ex. A wadded piece of paper will fall faster than a flat piece of paper which will experience more air resistance due to its larger surface area

69. An apple and a feather falling at the same rate absent air resistance (vacuum)

70. Free fall acceleration: Describe the acceleration of the object as it falls off the cliff – notice the change in velocity after each second of fall

71. Free fall acceleration: All objects, when thrown up will continue to move upward for some time, stop momentarily at the peak, and then change direction and begin to fall. Velocity at the top of the arc is 0 m/s

72. What goes up must come down!! In an upward displacement of an object, as soon as the ball is released with an initial positive velocity, it has an acceleration of -9.81m/s 2, causing the object to slow down until it stops momentarily. It then changes direction moving downward with an increasing velocity.

73. Distance vs. Time and Velocity vs. time graph of an object thrown up in the presence of gravity

74. 2.6 Freely Falling Bodies Example 10 A Falling Stone A stone is dropped from the top of a tall building. After 3.00s of free fall, what is the displacement, y, of the stone?

75. Example 10: A falling stone 2.6 Freely Falling Bodies

76. 2.6 Freely Falling Bodies Example 12 How High Does it Go? The referee tosses the coin up with an initial speed of 5.00m/s. In the absence of air resistance, how high does the coin go above its point of release?

77. Example 12: How high does it go? 2.6 Freely Falling Bodies

78. 2.6 Freely Falling Bodies Conceptual Example 15 Taking Advantage of Symmetry Does the pellet in part b strike the ground beneath the cliff with a smaller, greater, or the same speed as the pellet in part a?

79. 2.7 Graphical Analysis of Velocity and Acceleration

83. CLASS ASSIGNMENT / HOMEWORK I will not accept late work

84. position x as a function of time t Average velocity : (slope of the line) xx tt x1x1 x2x2 t1t1 t2t2 t x Displacement :