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

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

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4 Linear Motion “delta” means “the change in” 5. = final – initial

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

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4 Linear Motion 7. fixed means constant, unchanging.

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4 Linear Motion When is an object moving?

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

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4 Linear Motion Vectors and Scalars

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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

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4 Linear Motion 11. Magnitude means size

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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

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

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4 Linear Motion Travel around perimeter:

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4 Linear Motion Travel around perimeter: from A B

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4 Linear Motion Travel around perimeter: from A B C

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

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

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4 Linear Motion Distance = path length =

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4 Linear Motion Distance = path length =28 m

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

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

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

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

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

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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

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

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

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

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

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4 Linear Motion 4.2 Speed

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

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

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

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

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

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

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4 Linear Motion How can you calculate speed? 4.2 Speed

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

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

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

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

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

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

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

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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

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

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

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

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

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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

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

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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

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

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

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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

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

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4 Linear Motion How do you calculate acceleration? 4.4 Acceleration

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

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

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

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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

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

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

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

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

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4 Linear Motion 4.5 Free Fall: How Fast

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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

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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

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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

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

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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:

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

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

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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

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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

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4 Linear Motion 4.6 Free Fall: How Far

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

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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

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

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

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

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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

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4 Linear Motion V-t graph: slope = acceleration

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4 Linear Motion

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V-t graph: area under curve = displacement

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

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

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

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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

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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

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

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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

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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

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

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

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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

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

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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

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

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

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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

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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

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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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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