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4 Linear Motion 1. Motion of an object is described by its position, speed, direction, and acceleration.

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Presentation on theme: "4 Linear Motion 1. Motion of an object is described by its position, speed, direction, and acceleration."— Presentation transcript:

1 4 Linear Motion 1. Motion of an object is described by its position, speed, direction, and acceleration.

2 4 Linear Motion 2) MKS units are Meters, Kilograms Seconds

3 4 Linear Motion 3. Initial means “first” or “starting”

4 4 Linear Motion  “delta”  means “the change in” 5.  = final – initial

5 4 Linear Motion 6. wrt means “with respect to”

6 4 Linear Motion 7. fixed means constant, unchanging.

7 4 Linear Motion When is an object moving?

8 4 Linear Motion 8. An object is moving when its position changes relative to a fixed point. 4.1 Motion Is Relative

9 4 Linear Motion Vectors and Scalars

10 4 Linear Motion 9. Vectors or vector quantities have magnitude and direction 10.Scalars or scalar quantities have only magnitude 4.1 Motion Is Relative

11 4 Linear Motion 11. Magnitude means size

12 4 Linear Motion 12. Distance means total path length an object travels 13.Displacement means final position minus initial position 4.1 Motion Is Relative

13 4 Linear Motion 14. In symbols Displacement =  x  or  y 4.1 Motion Is Relative

14 4 Linear Motion Travel around perimeter:

15 4 Linear Motion Travel around perimeter: from A  B

16 4 Linear Motion Travel around perimeter: from A  B  C

17 4 Linear Motion Travel around perimeter: from A  B  C  D

18 4 Linear Motion Travel around perimeter: from A  B  C  D  A

19 4 Linear Motion Distance = path length =

20 4 Linear Motion Distance = path length =28 m

21 4 Linear Motion Distance = path length =28 m Displacment = 0

22 4 Linear Motion 15) Distance is a scalar and Displacement is a vector

23 4 Linear Motion 16. Motion is relative: we always describe motion relative to something else

24 4 Linear Motion 17. Usually we measure motion relative Earth’s surface

25 4 Linear Motion How can you tell if an object is moving? 4.1 Motion Is Relative

26 4 Linear Motion http://www.youtube.com/watch ?v=oRBchZLkQR0 http://www.youtube.com/watch ?v=KLd-rJMoeko http://www.youtube.com/watch ?v=xMF2CfYLomY

27 4 Linear Motion 18. Speed = distance time v = d t 4.2 Speed

28 4 Linear Motion 19. Before Galileo, people described motion as “slow” or “fast.” 4.2 Speed

29 4 Linear Motion 20.Galileo was the first to calculate speed 21. Speed is how fast an object moves 4.2 Speed

30 4 Linear Motion 22. MKS units of speed meters/second = m/sec. v = d t 4.2 Speed

31 4 Linear Motion 4.2 Speed

32 4 Linear Motion Instantaneous Speed 23. Instantaneous speed is the speed at an instant of time 24. Speedometer measures instantaneous speed. 4.2 Speed

33 4 Linear Motion The speedometer gives readings of instantaneous speed in both mi/h and km/h. 4.2 Speed

34 4 Linear Motion Average Speed 25. average speed =total distance total time. 4.2 Speed

35 4 Linear Motion Is average speed the same as instantaneous speed? 4.2 Speed

36 4 Linear Motion REARRANGE equation: v = d/t 26. HOW FAR: total distance d = average speed X total time d = v t

37 4 Linear Motion 27. Odometer measures how far an object travels.

38 4 Linear Motion How can you calculate speed? 4.2 Speed

39 4 Linear Motion 28. Velocity is speed in a specific direction. 4.3 Velocity

40 4 Linear Motion 29. MKS units of Velocity : m/sec 4.3 Velocity

41 4 Linear Motion 30. Velocity is the rate of change of position V =  x  t 4.3 Velocity

42 4 Linear Motion 31. Rate always means wrt time 4.3 Velocity

43 4 Linear Motion 32. Speed is a scalar; and Velocity is a vector. 4.3 Velocity

44 4 Linear Motion Constant Velocity 33. Constant velocity means traveling in a straight line at constant speed. 4.3 Velocity

45 4 Linear Motion Changing Velocity 34. Velocity changes if speed changes or direction changes or both change. 4.3 Velocity

46 4 Linear Motion The car on the circular track may have a constant speed but not a constant velocity, because its direction of motion is changing every instant. 4.3 Velocity

47 4 Linear Motion How is velocity different from speed? 4.3 Velocity

48 4 Linear Motion 35. Acceleration = change in velocity time interval a =  V  T

49 4 Linear Motion 36. Acceleration is the rate of change of velocity.

50 4 Linear Motion 37. Acceleration means decreases or increases in velocity. 38. Decreased acceleration is called deceleration. 4.4 Acceleration

51 4 Linear Motion 37. Acceleration means decreases OR increases in velocity. 38. Deceleration = decreased acceleration The brakes of a car cause deceleration. 4.4 Acceleration

52 4 Linear Motion Change in Direction 39. Acceleration is a vector quantity because it depends on direction 4.4 Acceleration

53 4 Linear Motion Change in Direction 40. REMEMBER Speed and velocity are NOT the same. Acceleration is the rate of change of velocity, NOT speed. Acceleration is a vector quantity because it has direction. 4.4 Acceleration

54 4 Linear Motion 41. Speed up: Accelerate in the same direction as velocity vectors:

55 4 Linear Motion 41. Speed up: Accelerate in the direction of velocity 42. Slow down: Accelerate against direction of velocity 4.4 Acceleration

56 4 Linear Motion 41. Speed up: Accelerate in the direction of velocity 42. Slow down: Accelerate against velocity 43: Change direction: Accelerate at an angle to velocity 4.4 Acceleration

57 4 Linear Motion Velocity units: meters/second = m/sec 44. MKS Acceleration units : meters/second = m/sec 2 second 4.4 Acceleration

58 4 Linear Motion How do you calculate acceleration? 4.4 Acceleration

59 4 Linear Motion 45. Free fall assumptions: A) no air resistance B) only gravity force affects motion of object

60 4 Linear Motion 46. Projectile = Object in free fall 47. Trajectory = path of projectile

61 4 Linear Motion Falling Objects 48. Time t is the time elapsed since projectile began to move. 4.5 Free Fall: How Fast

62 4 Linear Motion 49. Every second of free fall: instantaneous speed of object increases by ~ 10m /sec. V = 10 t 4.5 Free Fall: How Fast

63 4 Linear Motion 50. Acceleration of free fall =g g  10 m sec 2

64 4 Linear Motion 51. g is “acceleration due to gravity ” 52. g is NOT called “gravity”

65 4 Linear Motion 53. For more precise calculations use g = 9.8 m/sec 2

66 4 Linear Motion 54.HOW FAST: Instantaneous speed in free fall v = gt v = 10 t 4.5 Free Fall: How Fast

67 4 Linear Motion 4.5 Free Fall: How Fast

68 4 Linear Motion 55. Average projectile speed = V avg V avg = initial speed + final speed 2 V avg = V f + V i 2 4.5 Free Fall: How Fast

69 4 Linear Motion Rising Objects 56. A projectile thrown straight up: slows as it travels up. stops momentarily free falls back down 4.5 Free Fall: How Fast

70 4 Linear Motion 57. When projectile travels up: a) Velocity is ↑ acceleration= g ↓ b) Velocity DECREASES 10 m/sec every second 4.5 projectile moving straight up

71 4 Linear Motion 58. At highest point in trajectory, velocity = 0 acceleration = g ↓. 4.5 projectile moving straight up:

72 4 Linear Motion 59. when traveling back down, a) velocity ↓ ; acceleration =g ↓. b) velocity increases in 10 m/sec ↓ every second 4.5 projectile moving straight up:

73 4 Linear Motion 60. The change in speed in each second is the same going up or down 4.5 Free Fall: How Fast

74 4 Linear Motion What is the acceleration of an object in free fall? 4.5 Free Fall: How Fast

75 4 Linear Motion 61. Every second in free fall, a projectile falls further than it did the previous second. 4.6 Free Fall: How Far

76 4 Linear Motion 62. HOW FAR: distance a projectile free falls : d =½ gt 2 = ½ [10]t 2 =5 t 2 d = 5t 2 4.6 Free Fall: How Far

77 4 Linear Motion 4.6 Free Fall: How Far

78 4 Linear Motion 63. Galileo derived these kinematics equations experimentally v = at = 10 t and d = ½ at 2 = 5t 2

79 4 Linear Motion 64. Summary free fall on Earth a = g= 10 m/sec 2 how fast: v = at = 10 t how far: d = ½ at 2 = 5t 2

80 4 Linear Motion For a falling object, how does the distance per second change? 4.6 Free Fall: How Far

81 4 Linear Motion 65. Graphs visually describe relationships. 4.7 Graphs of Motion

82 4 Linear Motion 66. In motion graphs, time is ALWAYS on the x-axis

83 4 Linear Motion 67. On a speed-versus-time graph [v-t graph] the slope represents acceleration. 68. On a v-t graph, the area under the curve equals the total distance traveled. 4.7 Graphs of Motion graphing free fall

84 4 Linear Motion V-t graph: slope = acceleration

85 4 Linear Motion

86

87 V-t graph: area under curve = displacement

88 4 Linear Motion V-t graph: area under curve = displacement Area of triangle = ½ b h

89 4 Linear Motion area under curve: =½ base X height =½ [5 sec][50 m/sec]

90 4 Linear Motion area under curve: =½ base X height =½ [5 sec][50 m/sec] = 125 m

91 4 Linear Motion 69. linear relationship = straight line on v-t graph time and velocity are directly proportional 70. slope on v-t graph is constant 71. If t doubled, then v doubled V-T graph

92 4 Linear Motion 72. Displacement-Versus-Time in free fall d-t graph a) displacement d on Y axis b) Time on X axis 4.7 Graphs of Motion

93 4 Linear Motion 73. The d –t graph of free fall is parabolic. 4.7 Graphs of Motion

94 4 Linear Motion 74. The relationship between distance and time is nonlinear. The relationship is quadratic and the curve is parabolic 75. when t doubled, d is quadrupled. Distance depends on time squared! 4.7 Graphs of Motion

95 4 Linear Motion 76. The slope of the curved line is different at different points. 77. The slope on a d-t graph is velocity, the rate at which displacement is covered per unit of time. 78. The slope is steeper as time passes. This shows that speed increases with time. 4.7 Graphs of Motion

96 4 Linear Motion What does a slope of a speed-versus- time graph represent? 4.7 Graphs of Motion

97 4 Linear Motion 79. Air resistance is friction experienced by object in movement wrt air 4.8 Air Resistance and Falling Objects

98 4 Linear Motion 80. Air resistance noticeably slows the motion of objects with large surface areas like falling feathers or pieces of paper. 81. But air resistance is less noticeable on more compact objects like marbles and baseballs. 4.8 Air Resistance and Falling Objects

99 4 Linear Motion 82. If there is no air resistance, all objects free fall at same rate. 4.8 Air Resistance and Falling Objects

100 4 Linear Motion 83. If air resistance is small, it is negligible and we ignore it in our calculations. 4.8 Air Resistance and Falling Objects

101 4 Linear Motion How does air resistance affect falling objects? 4.8 Air Resistance and Falling Objects

102 4 Linear Motion Acceleration is the rate at which velocity itself changes. 4.9 How Fast, How Far, How Quickly How Fast Changes

103 4 Linear Motion 84. Remember Don’t mix up “how fast” with “how far.” How fast is as speed: v = gt. How far is a distance: d = 1/2gt 2 4.9 How Fast, How Far, How Quickly How Fast Changes

104 4 Linear Motion 85.Acceleration is not velocity, nor is it a change in velocity Acceleration is the RATE of change of velocity. 4.9 How Fast, How Far, How Quickly How Fast Changes

105 4 Linear Motion What is the relationship between velocity and acceleration? 4.9 How Fast, How Far, How Quickly How Fast Changes

106 4 Linear Motion 1.Jake walks east through a passenger car on a train that moves 10 m/s in the same direction. Jake’s speed relative to the car is 2 m/s. Jake’s speed relative to an observer at rest outside the train is a.2 m/s. b.5 m/s. c.8 m/s. d.12 m/s. Assessment Questions

107 4 Linear Motion 1.Jake walks east through a passenger car on a train that moves 10 m/s in the same direction. Jake’s speed relative to the car is 2 m/s. Jake’s speed relative to an observer at rest outside the train is a.2 m/s. b.5 m/s. c.8 m/s. d.12 m/s. Answer: D Assessment Questions

108 4 Linear Motion 2.A gazelle travels 2 km in a half hour. The gazelle’s average speed is a.1/2 km/h. b.1 km/h. c.2 km/h. d.4 km/h. Assessment Questions

109 4 Linear Motion 2.A gazelle travels 2 km in a half hour. The gazelle’s average speed is a.1/2 km/h. b.1 km/h. c.2 km/h. d.4 km/h. Answer: D Assessment Questions

110 4 Linear Motion 3.Constant speed in a constant direction is a.constant velocity. b.constant acceleration. c.instantaneous speed. d.average velocity. Assessment Questions

111 4 Linear Motion 3.Constant speed in a constant direction is a.constant velocity. b.constant acceleration. c.instantaneous speed. d.average velocity. Answer: A Assessment Questions

112 4 Linear Motion 4.A vehicle undergoes acceleration when it a.gains speed. b.decreases speed. c.changes direction. d.all of the above Assessment Questions

113 4 Linear Motion 4.A vehicle undergoes acceleration when it a.gains speed. b.decreases speed. c.changes direction. d.all of the above Answer: D Assessment Questions

114 4 Linear Motion 5.If a falling object gains 10 m/s each second it falls, its acceleration can be expressed as a.10 m/s/s. b.10 m/s 2. c.v = gt. d.both A and B. Assessment Questions

115 4 Linear Motion 5.If a falling object gains 10 m/s each second it falls, its acceleration can be expressed as a.10 m/s/s. b.10 m/s 2. c.v = gt. d.both A and B. Answer: D Assessment Questions

116 4 Linear Motion 6.A rock falls 180 m from a cliff into the ocean. How long is it in free fall? a.6 s b.10 s c.18 s d.180 s Assessment Questions

117 4 Linear Motion 6.A rock falls 180 m from a cliff into the ocean. How long is it in free fall? a.6 s b.10 s c.18 s d.180 s Answer: A Assessment Questions

118 4 Linear Motion 7.The slope of a speed-versus-time graph represents a.distance traveled. b.velocity. c.acceleration. d.air resistance. Assessment Questions

119 4 Linear Motion 7.The slope of a speed-versus-time graph represents a.distance traveled. b.velocity. c.acceleration. d.air resistance. Answer: C Assessment Questions

120 4 Linear Motion 8.In a vacuum tube, a feather is seen to fall as fast as a coin. This is because a.gravity doesn’t act in a vacuum. b.air resistance doesn’t act in a vacuum. c.greater air resistance acts on the coin. d.gravity is greater in a vacuum. Assessment Questions

121 4 Linear Motion 8.In a vacuum tube, a feather is seen to fall as fast as a coin. This is because a.gravity doesn’t act in a vacuum. b.air resistance doesn’t act in a vacuum. c.greater air resistance acts on the coin. d.gravity is greater in a vacuum. Answer: B Assessment Questions

122 4 Linear Motion 9.Speed and acceleration are actually a.one and the same concept, but expressed differently. b.rates of one another. c.entirely different concepts. d.expressions of distance traveled. Assessment Questions

123 4 Linear Motion 9.Speed and acceleration are actually a.one and the same concept, but expressed differently. b.rates of one another. c.entirely different concepts. d.expressions of distance traveled. Answer: C Assessment Questions

124 4 Linear Motion Check these calculations v = at so a = v/t a=50 m/sec = 10 m/sec 2 5 sec d = ½ gt 2 = 5t 2 = 5(5)5 d= 125 m


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