1. Motion of an object is described by its position ,

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1. Motion of an object is described by its position,

speed, direction, and acceleration.

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2) MKS units areMeters,

Kilograms Seconds

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3. Initial means “first” or “starting”

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“delta” means “the change in”

5. = final – initial

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6. wrt means “with respect to”

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7. fixed means constant, unchanging.

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When is an object moving?

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8. An object is moving when its position changes relative to a fixed point.

4.1 Motion Is Relative

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Vectors and Scalars

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9 . Vectors or vector quantities

have magnitude and direction

10.Scalars or scalar quantities

have only magnitude


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11. Magnitude means size

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12. Distance means total path length an object travels

13.Displacement means

final position minus initial position


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14. In symbols Displacement =xor y


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Travel around perimeter:

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from A B

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from A BC

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from A BC D

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from A BCDA

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Distance = path length =

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Distance = path length =28 m

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Distance = path length =28 m

Displacment = 0

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15) Distance is a scalar and

Displacement is a vector

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16. Motion is relative: we always describe motion

relative to something else

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17. Usually we measure motion relative Earth’s surface

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How can you tell if an object is moving?


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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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18. Speed = distance

time

v = d

t

4.2 Speed

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19. Before Galileo,

people described motion

as “slow” or “fast.”

4.2 Speed

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20.Galileo was the first to calculate speed

21. Speed is how fast an object moves

4.2 Speed

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22. MKS units of speed meters/second = m/sec .

v = d t

4.2 Speed

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4.2 Speed

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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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The speedometer gives readings of instantaneous speed in both mi/h and km/h.

4.2 Speed

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Average Speed

25. average speed

= total distance total time.

4.2 Speed

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Is average speed the same as instantaneous speed?

4.2 Speed

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REARRANGE equation: v = d/t

26. HOW FAR: total distance d

= average speed X total time

d = v • t

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27. Odometer measures how far an object travels.

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How can you calculate speed?

4.2 Speed

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28. Velocity is speed in a specific direction.

4.3 Velocity

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29. MKS units of Velocity : m/sec

4.3 Velocity

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30. Velocity is

the rate of change of position

V = x t

4.3 Velocity

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31. Rate always means wrt time

4.3 Velocity

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32. Speed is a scalar;

and Velocity is a vector.

4.3 Velocity

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Constant Velocity

33. Constant velocity means traveling in a straight line

at constant speed.

4.3 Velocity

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Changing Velocity

34. Velocity changes

if

speed changes

or direction changes

or both change .

4.3 Velocity

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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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How is velocity different from speed?

4.3 Velocity

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35. Acceleration = change in velocitytime interval

a = V T

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36. Acceleration is the rate of change of velocity.

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37. Acceleration means decreases or increases in velocity.

38. Decreased acceleration is called deceleration.

4.4 Acceleration

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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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Change in Direction

39 . Acceleration is

a vector quantity because it depends on direction

4.4 Acceleration

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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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41. Speed up: Accelerate in the same direction as velocity

vectors:

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41. Speed up: Accelerate in the direction of velocity

42. Slow down: Accelerate against direction of velocity

4.4 Acceleration

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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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Velocity units: meters/second = m/sec

44. MKS Acceleration units : meters/second = m/sec2

second

4.4 Acceleration

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How do you calculate acceleration?

4.4 Acceleration

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45. Free fall assumptions:A) no air resistanceB) only gravity force affects motion of object

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46. Projectile = Object in free fall

47. Trajectory = path of projectile

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Falling Objects

48. Time t is the time elapsed since projectile began to move.

4.5 Free Fall: How Fast

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49. Every second of free fall: instantaneous speed of object increases by ~ 10m /sec .

V = 10 t


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50. Acceleration of free fall =g

g 10 m sec2

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51. g is “acceleration due to gravity”

52. g is NOT called “gravity”

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53. For more precise calculations

use g = 9.8 m/sec2

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54. HOW FAST: Instantaneous speed in free fall

v = gt

v = 10 t


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55. Average projectile speed = Vavg

Vavg = initial speed + final speed

2

Vavg = Vf + Vi

2


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Rising Objects

56. A projectile thrown straight up: • slows as it travels up . • stops momentarily • free falls back down


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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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58. At highest point in trajectory,

velocity = 0 acceleration = g↓.

4.5 projectile moving straight up:

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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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60. The change in speed in each second

is the same

going up or down


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What is the acceleration of an object in free fall?


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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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62. HOW FAR: distance a projectile free falls :

d =½ gt2 = ½ [10]t2 =5 t2

d = 5t2


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63. Galileo derived these kinematics equations

experimentally

v = at = 10 t and d = ½ at2 = 5t2

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64. Summary free fall on Earth a = g= 10 m/sec2

how fast: v = at = 10 t how far: d = ½ at2 = 5t2

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For a falling object, how does the distance per second change?


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65. Graphs visually describe relationships.

4.7 Graphs of Motion

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66. In motion graphs, time is ALWAYS

on the x-axis

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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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V-t graph: slope = acceleration

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V-t graph: area under curve = displacement

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V-t graph: area under curve = displacement

Area of triangle =

½ b h

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area under curve:=½ base X height

=½ [5 sec][50 m/sec]

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area under curve:=½ base X height

=½ [5 sec][50 m/sec]= 125 m

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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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72. Displacement-Versus-Time in free fall

d-t graph

a) displacement d on Y axis

b) Time on X axis


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73. The d –t graph of free fall is parabolic.


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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!


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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.


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What does a slope of a speed-versus-time graph represent?


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79. Air resistance is friction experienced by object in movement wrt air

4.8 Air Resistance and Falling Objects

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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.


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82. If there is no air resistance, all objects free fall at same rate.


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83. If air resistance is small, it is negligible and we ignore it in our calculations.


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How does air resistance affect falling objects?


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Acceleration is the rate at which velocity itself changes.

4.9 How Fast, How Far, How Quickly How Fast Changes

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84. Remember

Don’t mix up “how fast” with “how far.”

• How fast is as speed: v = gt. • How far is a distance: d = 1/2gt2


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85.Acceleration is not velocity, nor is it a change in velocity

Acceleration is the RATE of change of velocity.


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What is the relationship between velocity and acceleration?


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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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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


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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.


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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


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3. Constant speed in a constant direction is

a. constant velocity.

b. constant acceleration.

c. instantaneous speed.

d. average velocity.


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3. Constant speed in a constant direction is

a. constant velocity.

b. constant acceleration.

c. instantaneous speed.

d. average velocity.

Answer: A


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4. A vehicle undergoes acceleration when it

a. gains speed.

b. decreases speed.

c. changes direction.

d. all of the above


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4. A vehicle undergoes acceleration when it

a. gains speed.

b. decreases speed.

c. changes direction.

d. all of the above

Answer: D


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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/s2.

c. v = gt.

d. both A and B.


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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/s2.

c. v = gt.

d. both A and B.

Answer: D


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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


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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


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7. The slope of a speed-versus-time graph represents

a. distance traveled.

b. velocity.

c. acceleration.

d. air resistance.


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7. The slope of a speed-versus-time graph represents

a. distance traveled.

b. velocity.

c. acceleration.

d. air resistance.

Answer: C


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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.


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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


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.


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


4 Linear Motion

Check these calculationsv = at so a = v/t a=50 m/sec = 10 m/sec2

5 sec d = ½ gt2 = 5t2 = 5(5)5d= 125 m

1. Motion of an object is described by its position ,

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