A presentation on velocity time graph and tickertapes

1. Kinematics 33

2.  A common way of analyzing the motion of
objects in physics labs is to perform a ticker
tape analysis.
Kinematics 34

3.  A ticker tape timer consists of an electrical
vibrator which vibrates 50 times per second.
 The time interval between two adjacent dots
on the ticker-tape is called one tick.
 One tick is equal to 1/50 s or 0.02 s.
Kinematics 35

4. Find the number of ticks and the time interval
between the first dot and the last dot on each
of the ticker tapes below. The frequency of the
ticker timer is equal to 50Hz.
Kinematics 36

5.  The trail of dots provides a history of the object's
motion and is therefore a representation of the
object's motion.
 The distance between dots on a ticker tape
represents the object's position change during
that time interval.
 A large distance between dots indicates that the
object was moving fast during that time interval.
 A small distance between dots means the object was
moving slow during that time interval.
Kinematics 37

6. Pattern Explanations
The distance between the dots is the
same. It shows that the object is moving
with constant speed.
The distance between the dots is short.
It shows that the speed of the object is
low.
The distance between the dots is far. It
shows that the object is moving at a high
speed
Kinematics 38

7.  The analysis of a ticker tape diagram will also
reveal if the object is moving with a constant
velocity or with a changing velocity
(accelerating).
Kinematics 39

8. Kinematics 40
Pattern Explanations
The distance between the dots is
increased. It shows that the speed of the
object increases.
The distance between the dots is
decreased. It shows that the speed of
the object decreases.

9. Kinematics 41

10.  Gradient = 0
Hence, velocity = 0
Kinematics 43

11.  Gradient is constant,
Hence, velocity is uniform
Kinematics 45

12.  Gradient is increasing
 Hence velocity is increasing.
Kinematics 47

13.  Gradient is decreasing
 Hence velocity is decreasing.
Kinematics 48

14. Kinematics 49
y-axis
x-axis
𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 =
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 − 𝑎𝑥𝑖𝑠
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 − 𝑎𝑥𝑖𝑠
𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 =
𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
𝑡𝑖𝑚𝑒
𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 = 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑜𝑏𝑗𝑒𝑐𝑡
∆𝑦
∆𝑥

15. Kinematics 50

16. Kinematics 52

17. Kinematics 54

18. Kinematics 56

19. Kinematics 57

20.  Increasing acceleration
Kinematics 58

21.  Decreasing acceleration
Kinematics 59

22. Kinematics 60
𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 =
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 − 𝑎𝑥𝑖𝑠
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 − 𝑎𝑥𝑖𝑠
𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 =
𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
𝑡𝑖𝑚𝑒
x-axis
y-axis
𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑜𝑏𝑗𝑒𝑐𝑡
∆𝑦
∆𝑥

23. Kinematics 61
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑅𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒 = 𝑊𝑖𝑑𝑡ℎ × 𝐿𝑒𝑛𝑔𝑡ℎ
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑅𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒 = 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 × 𝑇𝑖𝑚𝑒
width
length
𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 × 𝑇𝑖𝑚𝑒 = 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
𝐴𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑡ℎ𝑒 𝑔𝑟𝑎𝑝ℎ = 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡

24.  From the displacement-time graph
 Its gradient gives the velocity of the moving
object.
 From velocity-time graph
 Its gradient gives the acceleration of the moving
object.
 The area under the graph gives the distance
travelled by the object
Kinematics 62

25. 5
10
15
30 60 90 120
v
e
l
o
c
i
t
y
(
m
/
s
)
time(s)
goingupthehill
waitingat
trafficlights
Kinematics 63
Figure below shows the velocity a cyclist as she
cycled through a town.

26. 1. What was the cyclist’s velocity after 60 s?
2. How long did she have to wait at the traffic
light?
3. Which was larger, her deceleration as she
stopped at the traffic lights, or her
acceleration when she started again? Explain
your answer.
4. What is her total distance travelled for 120 s
of the journey?
Kinematics 64

27.  Figure below represents graphically the
velocity of a bus moving along a straight road
over a period of time.
Kinematics 65
0 20 40 60 80 100 t / s
10
20
30
40
v/ m/s
A
B C
D

28. 1. What does the portion of the graph
between 0 and A indicate?
2. What can you say about the motion of the
bus between B and C?
3. What is the acceleration of the bus
between C and D?
4. What is the total distance traveled by the
bus in 100 s?
5. What is the average velocity of the bus?
Kinematics 66

29.  The graph below shows how the velocity of a
certain body varies with time, t.
Kinematics 67
0
10
20
30
40
10 20 30 40 50
V
e
l
o
c
i
t
y
(
m
/
s
)
Time(s)

30. 1. Calculate the acceleration during the first
10 s shown on the graph.
2. During the period t = 30 s to t = 45 s the
body decelerates uniformly to rest.
Complete the graph and obtain the velocity
of the body when t = 38 s.
3. Obtain the distance travelled by the body
during the period t = 30 s and t = 45 s.
Kinematics 68

31.  A cyclist started from rest achieved a speed
of 10 m s-1 in 5 s. He then cycled at this
speed constantly for the next 15 s. Finally he
decelerate to complete his 30 s journey.
1. Sketch a velocity-time graph for the whole
journey?
2. Calculate his deceleration in the last 10
seconds of the journey.
3. Calculate the distance that he travelled during
the journey.
Kinematics 69

32. Kinematics 70
10
velocity (m/s)
time (s)
5 20 30

33. 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = 𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 𝑜𝑓 𝑔𝑟𝑎𝑝ℎ =
𝑦2 − 𝑦1
𝑥2 − 𝑥1
𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 =
10 − 0
20 − 30
𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 =
10
−10
= −1 𝑚/𝑠2
Kinematics 71

34. 𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 = 𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑔𝑟𝑎𝑝ℎ
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 =
1
2
(15 + 30)(10)
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 =
1
2
(45)(10) = 225 𝑚
Kinematics 72

35.  A locomotive pulling a train out from one
station travels along a straight horizontal
track towards another station. The following
describe the velocity of the train varies with
time over the whole journey.
 It started from rest and gain a speed of 40 ms-1 in
2 s.
 It then travel with this speed constantly for 10 s.
 Finally it decelerates and reach the other station
within 2 s.
Kinematics 73

36.  Using the information given
1. Sketch a velocity-time graph for this journey.
2. Find
1. the acceleration of the train in the first 2 s.
2. the total distance travel between the two stations.
3. the average velocity of the train.
Kinematics 74

37. Kinematics 75
40
velocity (m/s)
time (s)
2 12 14

38. 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = 𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 𝑜𝑓 𝑔𝑟𝑎𝑝ℎ =
𝑦2 − 𝑦1
𝑥2 − 𝑥1
𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 =
40 − 0
2 − 0
𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 =
40
2
= 20 𝑚/𝑠2
Kinematics 76

39. 𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 = 𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑔𝑟𝑎𝑝ℎ
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 =
1
2
(14 + 10)(40)
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 =
1
2
(24)(40) = 480 𝑚
Kinematics 77

40. 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 =
𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑑
𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 =
480
14
𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 34.3 𝑚/𝑠
Kinematics 78

41. 1. What must change when a body is
accelerating?
A. the force acting on the body
B. the mass of the body
C. the speed of the body
D. the velocity of the body
Kinematics 79

42. 2. Which of the following defines
acceleration?
Kinematics 80
A

43. 3. Which quantity X is calculated using this
equation?
A. acceleration
B. average velocity
C. distance travelled
D. speed
Kinematics 81

44. 4. A car is brought to rest in 5 s from a speed
of 10 m / s.
5. What is the average deceleration of the
car?
A. 0.5 m / s2
B. 2 m / s2
C. 15 m / s2
D. 50 m / s2
Kinematics 82

45. 5. A tennis player hits a ball over the net.
Kinematics 83

46. 1. In which position is the ball accelerating?
A. P and Q only
B. P and R only
C. Q and R only
D. P, Q and R
Kinematics 84

47. 6. The diagram shows a strip of paper tape
that has been pulled under a vibrating arm
by an object moving at constant speed. The
arm was vibrating regularly, making 50 dots
per second.
Kinematics 85

48. 1. What was the speed of the object?
A. 2.0 cm / s
B. 5.0 cm / s
C. 100 cm / s
D. 200 cm / s
Kinematics 86

49. 7. Which speed / time graph applies to an
object at rest?
Kinematics 87
D

50. 8. The speed-time graph shown is for a bus
travelling between stops.
9. Where on the graph is the acceleration of
the bus the greatest?
Kinematics 88
B

51. 9. A skier is travelling downhill. The
acceleration on hard snow is 4 m / s2 and
on soft snow is 2 m / s2.
10. Which graph shows the motion of the skier
when moving from hard snow to soft snow?
Kinematics 89

52. Kinematics 90
C

53. 10. The graph shows the speed of a car as it
accelerates from rest.
11. During part of this time the acceleration is
uniform.
Kinematics 91

54. 1. What is the size of this uniform
acceleration?
A. 5 m/s2
B. 6 m/s2
C. 10 m/s2
D. 20 m/s2
Kinematics 92

55. 11. The diagram shows a speed-time graph for
a body moving with constant acceleration.
Kinematics 93

56. 1. What is represented by the shaded area
under the graph?
A. acceleration
B. distance
C. speed
D. time
Kinematics 94

57. 12. The graph illustrates the motion of an
object.
Kinematics 95

58. 1. Which feature of the graph represents the
distance travelled by the object whilst
moving at a constant speed?
A. area S
B. area S + area T
C. area T
D. the gradient at point X
Kinematics 96

59. 13. A cyclist is riding along a road when an
animal runs in front of him. The graph
shows the cyclist’s motion. He sees the
animal at P, starts to brake at Q and stops
at R.
Kinematics 97

60. 1. What is used to find the distance travelled
after he applies the brakes?
A. the area under line PQ
B. the area under line QR
C. the gradient of line PQ
D. the gradient of line QR
Kinematics 98

61. 14. The diagram shows the speed-time graph
for an object moving at constant speed.
Kinematics 99

62. 1. What is the distance travelled by the
object in the first 3 s?
A. 1.5 m
B. 2.0 m
C. 3.0 m
D. 6.0 m
Kinematics 100

63. 15. A car accelerates from traffic lights. The
graph shows how the car’s speed changes
with time.
Kinematics 101

64. 1. How far does the car travel before it
reaches a steady speed?
A. 10 m
B. 20 m
C. 100 m
D. 200 m
Kinematics 102

65. 16. The graph represents the movement of a
body accelerating from rest.
Kinematics 103

66. 1. After 5 seconds how far has the body
moved?
A. 2 m
B. 10 m
C. 25 m
D. 50 m
Kinematics 104

67. 17. The graph shows the movement of a car
over a period of 50 s.
Kinematics 105

68. 1. What was the distance travelled by the car
during the time when it was moving at a
steady speed?
A. 10 m
B. 100 m
C. 200 m
D. 400 m
Kinematics 106

69. 18. The graph shows the movement of a car
over a period of 50 s.
Kinematics 107

70. 1. What was the distance travelled by the car
while its speed was increasing?
A. 10 m
B. 20 m
C. 100 m
D. 200 m
Kinematics 108

71. 19. The graph represents part of the journey of
a car.
Kinematics 109

72. 1. What distance does the car travel during
this part of the journey?
A. 150 m
B. 300 m
C. 600 m
D. 1200 m
Kinematics 110

73. Kinematics 111

74. Kinematics 112

75. Kinematics 113

76. Kinematics 114

77. Kinematics 115

78. Kinematics 116

79. Kinematics 117

80.  A free falling object is an object that is
falling under the sole influence of gravity.
 Any object that is being acted upon only by
the force of gravity is said to be in a state of
free fall.
Kinematics 118

81.  There are three important motion
characteristics that are true of free-
falling objects:
 Free-falling objects do not encounter air
resistance.
 All free-falling objects (on Earth) accelerate
downwards at a rate of 9.8 m/s2 (often
approximated as 10 m/s2)
 Not affected by mass and shape of the object.
Kinematics 119

82. Kinematics 120
Velocity
Time

83. Kinematics 121
At the start of his jump the
air resistance is zero so he
accelerate downwards.

84. Kinematics 122
As his speed increases his
air resistance will also
increase

85. Kinematics 123
Eventually the air resistance will be
big enough to balance the skydiver’s
weight.

86. How the forces change with time.
KEY
Gravity
(constant value &
always present…weight)
Air resistance
(friction)
Net force
(acceleration OR changing
velocity)

87.  The size of the air resistance on an object
depends on the area of the object and its
speed;
 the larger the area, the larger the air resistance.
 the faster the speed, the larger the air resistance.
Kinematics 125

88. Kinematics 126
When he opens his
parachute the air
resistance suddenly
increases, causing
him to start slow
down.

89. Kinematics 127
Because he is
slowing down his air
resistance will
decrease until it
balances his weight.
The skydiver has now
reached a new, lower
terminal velocity.

90. Velocity
Time
Speed
increases…
Terminal
velocity
reached…
Parachute opens –
diver slows down
New, lower terminal
velocity reached
Diver hits the
ground

91. 1. A small steel ball is dropped from a low
balcony.
Ignoring air resistance, which statement
describes its motion?
A. It falls with constant acceleration.
B. It falls with constant speed.
C. It falls with decreasing acceleration.
D. It falls with decreasing speed.
Kinematics 129

92. 2. A student drops a table-tennis ball in air.
1. What happens to the velocity and to the
acceleration of the ball during the first few
seconds after release?
Kinematics 130
C

93. 3. Two stones of different weight fall at the
same time from a table. Air resistance may
be ignored.
4. What will happen and why?
Kinematics 131
A

94. 4. The three balls shown are dropped from a
bench.
Which balls have the same acceleration?
A. aluminium and lead only
B. aluminium and wood only
C. lead and wood only
D. aluminium, lead and wood
Kinematics 132

95. 5. Which graph shows the motion of a heavy,
steel ball falling from a height of 2 m?
Kinematics 133
A

96. 6. A stone falls freely from the top of a cliff
into the sea. Air resistance may be ignored.
Which graph shows how the acceleration of
the stone varies with time as it falls?
Kinematics 134
D

97. 7. An object is falling under gravity with
terminal velocity.
What is happening to its speed?
A. It is decreasing to a lower value.
B. It is decreasing to zero.
C. It is increasing.
D. It is staying constant.
Kinematics 135

98. 8. The diagrams show a parachutist in four
positions after she jumps from a high balloon.
At which position does she have terminal
velocity?
Kinematics 136
C

99. 9. Which graph represents the motion of a
body falling vertically that reaches a
terminal velocity?
Kinematics 137
B

100. 10. The speed-time graph for a falling skydiver
is shown below. The skydiver alters his fall
first by spreading his arms and legs and
then by using a parachute.
11. Which part of the graph shows the diver
falling with terminal velocity?
Kinematics 138
D

101. (a) (i) weight or gravity
(ii) air resistance or drag or friction
Kinematics 139
(b) (i) 9.8 m/s2 or 10 m/s2
(ii) air resistance increases to oppose gravity
or air resistance increases as speed increases
(iii) air resistance = weight
or downward force balances upward force
or no resultant force

102. (a) (i) 9.8 m/s2 or 10 m/s2
Kinematics 140
(b) (i) air resistance = weight
or downward force balances upward force
or no resultant force
(ii) weight larger than air resistance
or downward force greater than upward force
(c) coin and paper accelerate at 10 m/s2
hit bottom at the same time
not fall at same time

103. (a) decelerating uniformly and comes to rest at 4 s
Kinematics 141
(b) (i) 40 m/s
(ii) 4 s
(c)
acceleration =
change in speed
time
acceleration =
40 − 0
4
acceleration = 10 m/s2
(c) distance = area under the graph
distance =
1
2
× 40 × 4
distance = 80 m

104. LEARNING OUTCOMES
Kinematics 142

105.  State what is meant by speed and velocity.
 Calculate average speed using distance
travelled/time taken.
 State what is meant by uniform acceleration
and calculate the value of an acceleration
using change in velocity/time taken.
 Discuss non-uniform acceleration.
Kinematics 143

106.  Plot and interpret speed-time and distance-
time graphs.
 Recognise from the shape of a speed-time
graph when a body is
 at rest,
 moving with uniform speed,
 moving with uniform acceleration,
 moving with non-uniform acceleration.
 Calculate the area under a speed-time graph
to determine the distance travelled for
motion with uniform speed or uniform
acceleration.
Kinematics 144

107.  State that the acceleration of free-fall for a
body near to the Earth is constant and is
approximately 10 m/s2.
 Describe qualitatively the motion of bodies
with constant weight falling with and without
air resistance (including reference to
terminal velocity).
Kinematics 145