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

4 Linear Motion

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

speed, direction, and acceleration.

4 Linear Motion

2) MKS units areMeters,

Kilograms Seconds

4 Linear Motion

3. Initial means “first” or “starting”

4 Linear Motion

“delta” means “the change in”

5. = final – initial

4 Linear Motion

6. wrt means “with respect to”

4 Linear Motion

7. fixed means constant, unchanging.

4 Linear Motion

When is an object moving?

4 Linear Motion

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

4.1 Motion Is Relative

4 Linear Motion

Vectors and Scalars

4 Linear Motion

9 . Vectors or vector quantities

have magnitude and direction

10.Scalars or scalar quantities

have only magnitude


4 Linear Motion

11. Magnitude means size

4 Linear Motion

12. Distance means total path length an object travels

13.Displacement means

final position minus initial position


4 Linear Motion

14. In symbols Displacement =xor y


4 Linear Motion

Travel around perimeter:

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from A B

4 Linear Motion


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 =

4 Linear Motion

Distance = path length =28 m

4 Linear Motion

Distance = path length =28 m

Displacment = 0

4 Linear Motion

15) Distance is a scalar and

Displacement is a vector

4 Linear Motion

16. Motion is relative: we always describe motion

relative to something else

4 Linear Motion

17. Usually we measure motion relative Earth’s surface

4 Linear Motion

How can you tell if an object is moving?


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

4 Linear Motion

18. Speed = distance

time

v = d

t

4.2 Speed

4 Linear Motion

19. Before Galileo,

people described motion

as “slow” or “fast.”

4.2 Speed

4 Linear Motion

20.Galileo was the first to calculate speed

21. Speed is how fast an object moves

4.2 Speed

4 Linear Motion

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

v = d t

4.2 Speed

4 Linear Motion

4.2 Speed

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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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

4 Linear Motion

Is average speed the same as instantaneous speed?

4.2 Speed

4 Linear Motion

REARRANGE equation: v = d/t

26. HOW FAR: total distance d

= average speed X total time

d = v • t

4 Linear Motion

27. Odometer measures how far an object travels.

4 Linear Motion

How can you calculate speed?

4.2 Speed

4 Linear Motion

28. Velocity is speed in a specific direction.

4.3 Velocity

4 Linear Motion

29. MKS units of Velocity : m/sec

4.3 Velocity

4 Linear Motion

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

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

4 Linear Motion

How is velocity different from speed?

4.3 Velocity

4 Linear Motion

35. Acceleration = change in velocitytime interval

a = V T

4 Linear Motion

36. Acceleration is the rate of change of velocity.

4 Linear Motion

37. Acceleration means decreases or increases in velocity.

38. Decreased acceleration is called deceleration.

4.4 Acceleration

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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Change in Direction

39 . Acceleration is

a vector quantity because it depends on direction

4.4 Acceleration

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

4 Linear Motion

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

vectors:

4 Linear Motion

41. Speed up: Accelerate in the direction of velocity

42. Slow down: Accelerate against direction of velocity

4.4 Acceleration

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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Velocity units: meters/second = m/sec

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

second

4.4 Acceleration

4 Linear Motion

How do you calculate acceleration?

4.4 Acceleration

4 Linear Motion

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

4 Linear Motion

46. Projectile = Object in free fall

47. Trajectory = path of projectile

4 Linear Motion

Falling Objects

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

4.5 Free Fall: How Fast

4 Linear Motion

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

V = 10 t


4 Linear Motion

50. Acceleration of free fall =g

g 10 m sec2

4 Linear Motion

51. g is “acceleration due to gravity”

52. g is NOT called “gravity”

4 Linear Motion

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


4 Linear Motion


4 Linear Motion

55. Average projectile speed = Vavg

Vavg = initial speed + final speed

2

Vavg = Vf + Vi

2


4 Linear Motion

Rising Objects

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


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

4 Linear Motion

58. At highest point in trajectory,

velocity = 0 acceleration = g↓.

4.5 projectile moving straight up:

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:

4 Linear Motion

60. The change in speed in each second

is the same

going up or down


4 Linear Motion

What is the acceleration of an object in free fall?


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

4 Linear Motion

62. HOW FAR: distance a projectile free falls :

d =½ gt2 = ½ [10]t2 =5 t2

d = 5t2


4 Linear Motion


4 Linear Motion

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

4 Linear Motion

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


4 Linear Motion

65. Graphs visually describe relationships.

4.7 Graphs of Motion

4 Linear Motion

66. In motion graphs, time is ALWAYS

on the x-axis

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

4 Linear Motion

V-t graph: slope = acceleration

4 Linear Motion

4 Linear Motion

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V-t graph: area under curve = displacement

4 Linear Motion

V-t graph: area under curve = displacement

Area of triangle =

½ b h

4 Linear Motion

area under curve:=½ base X height

=½ [5 sec][50 m/sec]

4 Linear Motion

area under curve:=½ base X height

=½ [5 sec][50 m/sec]= 125 m

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

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 Linear Motion

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


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 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 Linear Motion

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


4 Linear Motion

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

4.8 Air Resistance and Falling Objects

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 Linear Motion

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


4 Linear Motion

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


4 Linear Motion

How does air resistance affect falling objects?


4 Linear Motion

Acceleration is the rate at which velocity itself changes.

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

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 = 1/2gt2


4 Linear Motion

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

Acceleration is the RATE of change of velocity.


4 Linear Motion

What is the relationship between velocity and acceleration?


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

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


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.


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


4 Linear Motion

3. Constant speed in a constant direction is

a. constant velocity.

b. constant acceleration.

c. instantaneous speed.

d. average velocity.


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


4 Linear Motion

4. A vehicle undergoes acceleration when it

a. gains speed.

b. decreases speed.

c. changes direction.

d. all of the above


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


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/s2.

c. v = gt.

d. both A and B.


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/s2.

c. v = gt.

d. both A and B.

Answer: D


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


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


4 Linear Motion

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

a. distance traveled.

b. velocity.

c. acceleration.

d. air resistance.


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


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.


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


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

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

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