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

2. 2) MKS units are Meters, Kilograms Seconds

3. 3. Initial means “first” or “starting”

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

5. 6. wrt means “with respect to”

6. 7. fixed means constant, unchanging.

7. When is an object moving?

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

9. Vectors and Scalars

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

11. 11. Magnitude means size

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

13. 4.1 Motion Is Relative
14. In symbols Displacement = Dx or Dy

14. Travel around perimeter:

15. Travel around perimeter: from A B

16. Travel around perimeter: from A BC

17. Travel around perimeter: from A BC D

18. Travel around perimeter: from A BCDA

19. Distance = path length =

20. Distance = path length =28 m

21. Distance = path length =28 m Displacment = 0

22. 15) Distance is a scalar and Displacement is a vector

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

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

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

26. http://www. youtube. com/watch. v=oRBchZLkQR0 http://www. youtube

27. 4.2 Speed
18. Speed = distance
time
v = d t

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

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

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

31. 4.2 Speed

32. 23. Instantaneous speed is the speed at an instant of time
24. Speedometer measures instantaneous speed.

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

34. = total distance total time.
4.2 Speed
Average Speed
average speed
= total distance total time.

35. Is average speed the same as instantaneous speed?

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

37. 27. Odometer measures how far an object travels.

38. 4.2 Speed
How can you calculate speed?

39. 28. Velocity is speed in a specific direction.

40. 29. MKS units of Velocity : m/sec

41. the rate of change of position V = Dx Dt
4.3 Velocity
30. Velocity is
the rate of change of position
V = Dx Dt

42. 31. Rate always means wrt time
4.3 Velocity
31. Rate always means wrt time

43. and Velocity is a vector.
32. Speed is a scalar;
and Velocity is a vector.

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

45. 34. Velocity changes if speed changes or direction changes
Changing Velocity
34. Velocity changes if
speed changes
or direction changes
or both change .

46. 4.3 Velocity
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.

47. 4.3 Velocity
How is velocity different from speed?

48. 35. Acceleration = change in velocity time interval a = DV DT

49. 36. Acceleration is the rate of change of velocity.

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

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

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

53. 4.4 Acceleration 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 .

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

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

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

57. 4.4 Acceleration Velocity units: meters/second = m/sec
44. MKS Acceleration units : meters/second = m/sec2
second

58. 4.4 Acceleration
How do you calculate acceleration?

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

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

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

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

63. 50. Acceleration of free fall =g g  10 m sec2

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

65. 53. For more precise calculations use g = 9.8 m/sec2

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

67. 4.5 Free Fall: How Fast

68. 4.5 Free Fall: How Fast 55. Average projectile speed = Vavg
Vavg = initial speed + final speed 2
Vavg = Vf + Vi

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

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

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

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

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

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

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

76. d =½ gt2 = ½ [10]t2 =5 t2 d = 5t2 4.6 Free Fall: How Far
62. HOW FAR: distance a projectile free falls :
d =½ gt2 = ½ [10]t2 =5 t2
d = 5t2

77. 4.6 Free Fall: How Far

78. 63. Galileo derived these kinematics equations experimentally v = at = 10 t and d = ½ at2 = 5t2

79. 64. Summary free fall on Earth a = g= 10 m/sec2 how fast: v = at = 10 t how far: d = ½ at2 = 5t2

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

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

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

83. 4.7 Graphs of Motion
graphing free fall
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.

84. V-t graph: slope = acceleration

87. V-t graph: area under curve = displacement

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

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

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

91. V-T graph 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

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

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

94. 4.7 Graphs of 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!

95. 4.7 Graphs of 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.

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

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

98. 4.8 Air Resistance and Falling Objects
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.

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

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

101. 4.8 Air Resistance and Falling Objects
How does air resistance affect falling objects?

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

103. 4.9 How Fast, How Far, How Quickly How Fast Changes
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

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

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

106. Assessment Questions
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
2 m/s.
5 m/s.
8 m/s.
12 m/s.

107. Assessment Questions
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
2 m/s.
5 m/s.
8 m/s.
12 m/s.
Answer: D

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

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

110. Assessment Questions Constant speed in a constant direction is
constant velocity.
constant acceleration.
instantaneous speed.
average velocity.

111. Assessment Questions Constant speed in a constant direction is
constant velocity.
constant acceleration.
instantaneous speed.
average velocity.
Answer: A

112. Assessment Questions A vehicle undergoes acceleration when it
gains speed.
decreases speed.
changes direction.
all of the above

113. Assessment Questions A vehicle undergoes acceleration when it
gains speed.
decreases speed.
changes direction.
all of the above
Answer: D

114. Assessment Questions
If a falling object gains 10 m/s each second it falls, its acceleration can be expressed as
10 m/s/s.
10 m/s2.
v = gt.
both A and B.

115. Assessment Questions
If a falling object gains 10 m/s each second it falls, its acceleration can be expressed as
10 m/s/s.
10 m/s2.
v = gt.
both A and B.
Answer: D

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

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

118. Assessment Questions The slope of a speed-versus-time graph represents
distance traveled.
velocity.
acceleration.
air resistance.

119. Assessment Questions The slope of a speed-versus-time graph represents
distance traveled.
velocity.
acceleration.
air resistance.
Answer: C

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

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

122. Assessment Questions Speed and acceleration are actually
one and the same concept, but expressed differently.
rates of one another.
entirely different concepts.
expressions of distance traveled.

123. Assessment Questions Speed and acceleration are actually
one and the same concept, but expressed differently.
rates of one another.
entirely different concepts.
expressions of distance traveled.
Answer: C

124. Check these calculations v = at so a = v/t a=50 m/sec = 10 m/sec sec d = ½ gt2 = 5t2 = 5(5)5 d= 125 m