This presentation can be used in introducing kinematics in 1 dimension. It includes distance, displacement, speed, velocity, acceleration and graphs of motion.

1. Rectilinear Kinematics
Motion in one dimension

2. Speed

3. Speed
• Most common student definition of speed:
Speed is how fast an object moves.

4. Speed
• Most common student definition of speed:
Speed is how fast an object moves.

5. Speed
• Most common student definition of speed:
Speed is how fast an object moves.
• My question: How fast is the car moving?

7. What (information? equipment?) do we need in order to
describe the motion of the car?

8. What (information? equipment?) do we need in order to
describe the motion of the car?
Clock Reading:

9. What (information? equipment?) do we need in order to
describe the motion of the car?
Clock Reading:

10. What (information? equipment?) do we need in order to
describe the motion of the car?
Clock Reading:
Is time enough to describe “how fast” the car moves?

11. What (information? equipment?) do we need in order to
describe the motion of the car?

12. What (information? equipment?) do we need in order to
describe the motion of the car?
Position:

13. What (information? equipment?) do we need in order to
describe the motion of the car?
Position:

14. What (information? equipment?) do we need in order to
describe the motion of the car?
Position:
What do we know about the motion?

16. Position + Clock Reading = Event

17. Position + Clock Reading = Event
• I’ll stop the movie and just show you 1
frame - there is a position and clock
reading associated with it.

18. Position + Clock Reading = Event
• I’ll stop the movie and just show you 1
frame - there is a position and clock
reading associated with it.

19. Position + Clock Reading = Event
• I’ll stop the movie and just show you 1
frame - there is a position and clock
reading associated with it.
Instantaneous Position

20. Position + Clock Reading = Event
• I’ll stop the movie and just show you 1
frame - there is a position and clock
reading associated with it.
Instantaneous Position How long is an “instant”?

21. Position + Clock Reading = Event

22. Position + Clock Reading = Event
• What can I do with 2 such events of an
object that is in motion? Think!

23. Position + Clock Reading = Event
• What can I do with 2 such events of an
object that is in motion? Think!

24. Position + Clock Reading = Event
• What can I do with 2 such events of an
object that is in motion? Think!

26. Average Velocity

27. Average Velocity
position “s” (m)

28. Average Velocity
position “s” (m)
clock reading (or instant) “t” (s)

29. Average Velocity
position “s” (m)
clock reading (or instant) “t” (s)
!!
! ! ! !! !

30. Average Velocity
position “s” (m)
clock reading (or instant) “t” (s)
!!
! ! ! !! !
What if I invert the values? What does it mean?

31. Average Velocity
position “s” (m)
clock reading (or instant) “t” (s)
!!
! ! ! !! !
What if I invert the values? What does it mean?
Create a name for this new defined quantity.

32. Rectilinear Kinematics
Motion in one dimension
Part II

33. How can we
understand Motion?

34. How can we
understand Motion?
• describe it verbally

35. How can we
understand Motion?
• describe it verbally
• solve it algebraically

36. How can we
understand Motion?
• describe it verbally
• solve it algebraically
• visualize it graphically

37. Graphs

38. Graphs
• What is the big deal? Everyone can learn
how to interpret and construct one.

39. Graphs
• What is the big deal? Everyone can learn
how to interpret and construct one.
• It will help you visualize and solve problems

40. Graphs
• What is the big deal? Everyone can learn
how to interpret and construct one.
• It will help you visualize and solve problems
• You must be very careful on your
interpretation of graphs

41. s vs. t graphs
10
9
position vs. time
8
7
6
position / m
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
clock reading / s

42. s vs. t graphs
10
9
position vs. time
8
7
6
position / m
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
clock reading / s

43. s vs. t graphs
10
9
position vs. time
8
y = 0.5x + 1.5 R² = 1
7
6
position / m
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
clock reading / s

44. s vs. t graphs
10
9
position vs. time
8
7
6
position / m
5
(7,5)
4
3
2
(1,2)
1
0
0 1 2 3 4 5 6 7 8 9 10
clock reading / s

45. 10
9
position vs. time
8
7
6
position / m
5
(7,5)
4
3
2
(1,2)
1
0
0 1 2 3 4 5 6 7 8 9 10
clock reading / s

46. 10
9
position vs. time
8
7
6
position / m 5
(7,5)
4
3
2
(1,2)
1
0
0 1 2 3 4 5 6 7 8 9 10
clock reading / s

47. 10
9
position vs. time
8
7
6
position / m 5
(7,5)
4
3
2
(1,2)
1
0
0 1 2 3 4 5 6 7 8 9 10
clock reading / s
!! !! ! !!
!! ! ! !!!!!" !! !
!! !! ! !!

48. !! !! ! !!
!! ! ! !!!!!" !! !
!! !! ! !!

49. !! !! ! !!
!! ! ! !!!!!" !! !
!! !! ! !!

50. !! !! ! !!
!! ! ! !!!!!" !! !
!! !! ! !!
10
9
position vs. time
8
y = 0.5x + 1.5 R² = 1
7
6
position / m
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
clock reading / s

51. !! !! ! !!
!! ! ! !!!!!" !! !
!! !! ! !!
10
9
position vs. time
8
y = 0.5x + 1.5 R² = 1
7
6
position / m
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
clock reading / s

52. !! !! ! !!
!! ! ! !!!!!" !! !
!! !! ! !!
10
9
position vs. time
8
y = 0.5x + 1.5 R² = 1
7
6
position / m
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
clock reading / s
slope (gradient) = average velocity

53. Take a look at this position vs. time graph!
10
9
8
7
6
position /m
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time/s

54. Take a look at this position vs. time graph!
10
9
8
7
6
position /m
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time/s

55. Take a look at this position vs. time graph!
10
9
8
7
6
position /m
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time/s

56. Take a look at this position vs. time graph!
10
9
8
7
6
position /m
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time/s

57. Take a look at this position vs. time graph!
10
9
8
7
6
position /m
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time/s

58. Take a look at this position vs. time graph!
10
9
8
7
6
position /m
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time/s
when the time interval decreases to zero
we get instantaneous velocity

59. Take a look at this position vs. time graph!
10
9
8
7
6
position /m
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time/s
when the time interval decreases to zero
we get instantaneous velocity

60. 10
9
8
7
6
position /m
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time/s

61. 10
9
8
7
position /m 6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time/s

62. 10
9
8
7
position /m 6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time/s
the gradient (slope) of the tangential line at an instant in
time gives you the instantaneous velocity

63. To conclude:

64. To conclude:
• The slope of the line connecting 2 events in
a positions vs. time graph gives you the
average velocity

65. To conclude:
• The slope of the line connecting 2 events in
a positions vs. time graph gives you the
average velocity
• If the time interval of these events go to
zero, we get a tangential line, at a instant in
time, whose slope is what we call
instantaneous velocity (e.g. speedometer)

66. Rectilinear Kinematics
Motion in one dimension
Part III

67. Uniform Velocity

68. Uniform Velocity
• same change in position for each (one)
second of the motion.

69. Uniform Velocity
• same change in position for each (one)
second of the motion.
• a.k.a constant velocity

70. Uniform Velocity
• same change in position for each (one)
second of the motion.
• a.k.a constant velocity
• average velocity is essentially the same as
uniform velocity

71. Velocity Graphs
10
Velocity vs. Time
9
8
7
velocity / ms-1
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time / s

72. Velocity Graphs
10
Velocity vs. Time
9
8
7
velocity / ms-1
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time / s

73. Velocity Graphs
10
Velocity vs. Time
9
8
7
velocity / ms-1
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time / s

74. Velocity Graphs
10
Velocity vs. Time
9
8
7
velocity / ms-1
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time / s

75. Velocity Graphs
10
Velocity vs. Time
9
8
7
velocity / ms-1
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time / s

76. Velocity Graphs
10
Velocity vs. Time
9
8
7
velocity / ms-1
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time / s
Uniform velocity: no change in speed!

77. Velocity Graphs
10
Velocity vs. Time
9
8
7
velocity / ms-1
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time / s
Uniform velocity: no change in speed!
Question: If particle moves at constant 3ms-1 for a time of
9s how much distance has it moved?

78. Velocity Graphs
10
Velocity vs. Time
9
8
7
velocity / ms-1
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time / s

79. Velocity Graphs
10
Velocity vs. Time
9
8
7
velocity / ms-1
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time / s

80. Velocity Graphs
10
Velocity vs. Time
9
8
7
velocity / ms-1
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
time / s

81. Velocity Graphs
10
Velocity vs. Time
9
8
7
velocity / ms-1
6
5
4
3
2
1
!"#! ! !!!!! ! !"!
0
0 1 2 3 4 5 6 7 8 9 10
time / s

82. Velocity Graphs
10
Velocity vs. Time
9
8
7
velocity / ms-1
6
5
4
3
2
1
!"#! ! !!!!! ! !"!
0
0 1 2 3 4 5 6 7 8 9 10
time / s
Units?

83. Velocity Graphs
10
Velocity vs. Time
9
8
7
velocity / ms-1
6
5
4
3
2
1
!"#! ! !!!!! ! !"!
0
0 1 2 3 4 5 6 7 8 9 10
time / s
Units? ms-1 x s = m

84. Uniform Velocity Graph

85. Uniform Velocity Graph
• its v vs. t is a horizontal line

86. Uniform Velocity Graph
• its v vs. t is a horizontal line
• the area below the line represents the
change in position

87. Uniform Velocity Graph
• its v vs. t is a horizontal line
• the area below the line represents the
change in position
• + and - signs may be used to represent
direction of motion

88. Usain Bolt - fastest man
alive

89. Warning

90. Warning

91. Warning
Just sitting on your A$$ watching cool videos may cause
brain damage!

92. Let’s do some physics
analysis

93. Let’s do some physics
analysis
• What is his average velocity? Calculate

94. Let’s do some physics
analysis
• What is his average velocity? Calculate
• What is his top instantaneous velocity?

95. Let’s do some physics
analysis
• What is his average velocity? Calculate
• What is his top instantaneous velocity?
• When in the race does he reach his top
velocity?

96. Let’s do some physics
analysis
• What is his average velocity? Calculate
• What is his top instantaneous velocity?
• When in the race does he reach his top
velocity?
• Any ideas to find his top velocity? and
when?

97. Let’s do some physics
analysis
• What is his average velocity? Calculate
• What is his top instantaneous velocity?
• When in the race does he reach his top
velocity?
• Any ideas to find his top velocity? and
when?
In groups, try to use this chart to extract as much
information as possible and be ready to present your
findings to the rest of the class.

100. Quick remarks about the fastest man alive:

101. Quick remarks about the fastest man alive:
• His top velocity was around 12.3 ms-1( 45 km/h,
28 mi/h)

102. Quick remarks about the fastest man alive:
• His top velocity was around 12.3 ms-1( 45 km/h,
28 mi/h)
• He reached his top speed at around 65 m

103. Quick remarks about the fastest man alive:
• His top velocity was around 12.3 ms-1( 45 km/h,
28 mi/h)
• He reached his top speed at around 65 m
• He took 41 steps in the race (about 4.3 steps
per second at an average step length of 2.5 m,
2.8 at peak velocity)

104. Quick remarks about the fastest man alive:
• His top velocity was around 12.3 ms-1( 45 km/h,
28 mi/h)
• He reached his top speed at around 65 m
• He took 41 steps in the race (about 4.3 steps
per second at an average step length of 2.5 m,
2.8 at peak velocity)
• his record is 0.13s faster than the second fastest
time. Insane!

105. Rectilinear Kinematics
Motion in one dimension
Part IV

107. Bugatti Veyron 16.4
Fastest road-legal car in the world

108. Bugatti Veyron 16.4
Fastest road-legal car in the world
• 0-100 km/h in 2.46s

109. Bugatti Veyron 16.4
Fastest road-legal car in the world
• 0-100 km/h in 2.46s
• Top speed of 431 km/h

110. Bugatti Veyron 16.4
Fastest road-legal car in the world
• 0-100 km/h in 2.46s
• Top speed of 431 km/h
• Cost: U$2,700,000

111. Bugatti Veyron 16.4
Fastest road-legal car in the world
• 0-100 km/h in 2.46s
• Top speed of 431 km/h
• Cost: U$2,700,000
• Number of unit sales in 2010: 40

112. Bugatti Veyron 16.4
Fastest road-legal car in the world
• 0-100 km/h in 2.46s
• Top speed of 431 km/h
• Cost: U$2,700,000
• Number of unit sales in 2010: 40

113. Bugatti Veyron 16.4
Fastest road-legal car in the world
• 0-100 km/h in 2.46s
• Top speed of 431 km/h
• Cost: U$2,700,000
• Number of unit sales in 2010: 40
What can we find out with this information?

114. Free Fall

115. Free Fall
• Have you heard of the number 10 m/s-2 in
association with free fall?

116. Free Fall
• Have you heard of the number 10 m/s-2 in
association with free fall?
• What does this number mean? What does
it describe?

117. Free Fall
• Have you heard of the number 10 m/s-2 in
association with free fall?
• What does this number mean? What does
it describe?
• Does it have any relation to kinematic
concepts we have defined?

118. Free Fall
• Have you heard of the number 10 m/s-2 in
association with free fall?
• What does this number mean? What does
it describe?
• Does it have any relation to kinematic
concepts we have defined?
• If I drop a ball from rest (zero velocity),
what is the velocity at the end of 1
second? ....

119. Acceleration: the change of velocity per (one) unit of
time

120. Acceleration: the change of velocity per (one) unit of
time
acceleration is a vector unit is ms-2

121. Acceleration: the change of velocity per (one) unit of
time
acceleration is a vector unit is ms-2
!!
!! !
!!

122. Acceleration: the change of velocity per (one) unit of
time
acceleration is a vector unit is ms-2
!!
!! !
!!

123. Acceleration: the change of velocity per (one) unit of
time
acceleration is a vector unit is ms-2
!!
!! !
!!
Note that the velocity on the definition of
acceleration is an instantaneous value (at an instant
in time)

124. Acceleration: the change of velocity per (one) unit of
time
acceleration is a vector unit is ms-2
!!
!! !
!!
Note that the velocity on the definition of
acceleration is an instantaneous value (at an instant
in time)
The acceleration found that way is an average value

125. Acceleration and sign
(+ or -) Direction

126. Acceleration and sign
(+ or -) Direction

127. Acceleration and sign
(+ or -) Direction
• An object moving in the (+) direction
has an acceleration

128. Acceleration and sign
(+ or -) Direction
• An object moving in the (+) direction
has an acceleration
• Same object moving in the (+) direction,
decelerates (slow down)

129. Acceleration and sign
(+ or -) Direction
• An object moving in the (+) direction
has an acceleration
• Same object moving in the (+) direction,
decelerates (slow down)
• An object moving in the (-) direction
accelerates

130. Acceleration and sign
(+ or -) Direction
• An object moving in the (+) direction
has an acceleration
• Same object moving in the (+) direction,
decelerates (slow down)
• An object moving in the (-) direction
accelerates
• Same object moving in the (-) direction
decelerates.

131. Summary

132. Summary
If the initial velocity has the same sign (direction) as the
acceleration, the object gets faster.

133. Summary
If the initial velocity has the same sign (direction) as the
acceleration, the object gets faster.
u

134. Summary
If the initial velocity has the same sign (direction) as the
acceleration, the object gets faster.
u
+

135. Summary
If the initial velocity has the same sign (direction) as the
acceleration, the object gets faster.
u a
+

136. Summary
If the initial velocity has the same sign (direction) as the
acceleration, the object gets faster.
u a
+ =

137. Summary
If the initial velocity has the same sign (direction) as the
acceleration, the object gets faster.
u a v
+ =

138. Summary
If the initial velocity has the same sign (direction) as the
acceleration, the object gets faster.
u a v
+ =
If the initial velocity has the opposite sign (direction) as the
acceleration, the object slows down.

139. Summary
If the initial velocity has the same sign (direction) as the
acceleration, the object gets faster.
u a v
+ =
If the initial velocity has the opposite sign (direction) as the
acceleration, the object slows down.
u

140. Summary
If the initial velocity has the same sign (direction) as the
acceleration, the object gets faster.
u a v
+ =
If the initial velocity has the opposite sign (direction) as the
acceleration, the object slows down.
u
+

141. Summary
If the initial velocity has the same sign (direction) as the
acceleration, the object gets faster.
u a v
+ =
If the initial velocity has the opposite sign (direction) as the
acceleration, the object slows down.
u a
+

142. Summary
If the initial velocity has the same sign (direction) as the
acceleration, the object gets faster.
u a v
+ =
If the initial velocity has the opposite sign (direction) as the
acceleration, the object slows down.
u a
+ =

143. Summary
If the initial velocity has the same sign (direction) as the
acceleration, the object gets faster.
u a v
+ =
If the initial velocity has the opposite sign (direction) as the
acceleration, the object slows down.
u a v
+ =

144. Non-uniform Velocity
Graphs
10
Velocity vs. Time
9
8
7
6
velocity / ms-1
5
4
3
2
1
0
0 1 2 3 4 5 6
time / s

145. Non-uniform Velocity
Graphs
10
Velocity vs. Time
9
8
7
6
velocity / ms-1
5
4
3
2
1
0
0 1 2 3 4 5 6
time / s

146. Non-uniform Velocity
Graphs
10
Velocity vs. Time
9
8
7
6
velocity / ms-1
5
4
3
2
1
0
0 1 2 3 4 5 6
time / s

147. Non-uniform Velocity
Graphs
10
Velocity vs. Time
9
8
7
6
velocity / ms-1
5
4
3
2
1
0
0 1 2 3 4 5 6
time / s

148. Non-uniform Velocity
Graphs
10
Velocity vs. Time
9
8
7
6
velocity / ms-1
5
4
3
2
1
0
0 1 2 3 4 5 6
time / s

149. Non-uniform Velocity
Graphs
10
Velocity vs. Time
9
8
7
6
velocity / ms-1
5
4
3
2
1
0
0 1 2 3 4 5 6
time / s

150. Non-uniform Velocity
Graphs
10
Velocity vs. Time
9
8
7
6
velocity / ms-1
5
4
3
2
1
0
0 1 2 3 4 5 6
time / s
How much is the speed changing each second?

151. Non-uniform Velocity
Graphs
10
Velocity vs. Time
9
8
7
6
velocity / ms-1
5
4
3
∆v = 8 - 5 = 1.5
2
∆t 4-2
1
0
0 1 2 3 4 5 6
time / s

152. Non-uniform Velocity
Graphs
10
Velocity vs. Time
9
8
7
6
velocity / ms-1
5
4
3
∆v = 8 - 5 = 1.5
2
∆t 4-2
1
0
0 1 2 3 4 5 6
time / s
The slope (gradient) is the acceleration

153. What was the change in position in these
5 seconds?
10
Velocity vs. Time
9
8
7
6
velocity / ms-1
5
4
3
2
1
0
0 1 2 3 4 5 6
time / s

154. What was the change in position in these
5 seconds?
10
Velocity vs. Time
9
8
7
6
velocity / ms-1
5
4
3
2
1
0
0 1 2 3 4 5 6
time / s
The area under the line is the change in position

155. What was the change in position in these
5 seconds?
10
Velocity vs. Time
9
8
7
6
velocity / ms-1
5
4
3
2
1
0
0 1 2 3 4 5 6
time / s
The area under the line is the change in position

156. What was the change in position in these
5 seconds?
10
Velocity vs. Time
9
8
7
6
velocity / ms-1
5
!
4 !! ! ! !!! ! !"!!!!
!
3
2
1 !! ! !!! ! !"!!
0
0 1 2 3 4 5 6
time / s

157. What was the change in position in these
5 seconds?
10
Velocity vs. Time
9
8
7
6
velocity / ms-1
5
!
4 !! ! ! !!! ! !"!!!!
!
3
2
1 !! ! !!! ! !"!!
0
0 1 2 3 4 5 6
time / s
There was a total displacement of 28.8m in 5 seconds

158. Motion Graphs
30 10
25 8
acceleration / ms-2
velocity / ms-1
20
6
15
4
10
2
5
0 0
0 1 2 3 4 5 6 0 1 2 3 4 5 6
time / s time / s
70
60
50
position / m
40
30
20
10
0
0 1 2 3 4 5 6
time / s

159. Motion Graphs
30
25
velocity / ms-1
20
15
10
5
0
0 1 2 3 4 5 6
time / s

160. Motion Graphs
30 10
25 8
acceleration / ms-2
velocity / ms-1
20
6
15
4
10
2
5
0 0
0 1 2 3 4 5 6 0 1 2 3 4 5 6
time / s time / s

161. Motion Graphs
30 10
25 8
acceleration / ms-2
velocity / ms-1
20
6
15
4
10
2
5
0 0
0 1 2 3 4 5 6 0 1 2 3 4 5 6
time / s time / s
70
60
50
position / m
40
30
20
10
0
0 1 2 3 4 5 6
time / s

162. Motion Graphs
30 10
25 8
acceleration / ms-2
velocity / ms-1
20
6
15
4
10
2
5
0 0
0 1 2 3 4 5 6 0 1 2 3 4 5 6
time / s time / s
70
60
50
position / m
40
30
20
10
0
0 1 2 3 4 5 6
time / s

163. Motion Graphs
30 10
25 8
acceleration / ms-2
velocity / ms-1
20
6
15
4
10
2
5
0 0
0 1 2 3 4 5 6 0 1 2 3 4 5 6
time / s time / s
70
60
50
position / m
40
30
20
10
0
0 1 2 3 4 5 6
time / s

164. Motion Graphs
30 10
25 8
acceleration / ms-2
velocity / ms-1
20
6
15
4
10
2
5
0 0
0 1 2 3 4 5 6 0 1 2 3 4 5 6
time / s time / s
70
60
50
position / m
40
30
20
10
0
0 1 2 3 4 5 6
time / s

165. Motion Graphs
10
8
acceleration / ms-2
6
4
2
0
0 1 2 3 4 5 6
time / s
70
60
50
position / m
40
30
20
10
0
0 1 2 3 4 5 6
time / s

166. Motion Graphs
10
8
acceleration / ms-2
6
4
2
0
0 1 2 3 4 5 6
time / s
70
60
50
position / m
40
30
20
10
0
0 1 2 3 4 5 6
time / s

167. Motion Graphs
10
8
acceleration / ms-2
6
4
2
0
0 1 2 3 4 5 6
time / s
70
60
50
position / m
40
30
20
10
0
0 1 2 3 4 5 6
time / s

168. Motion Graphs
30 10
25 8
acceleration / ms-2
velocity / ms-1
20
6
15
4
10
2
5
0 0
0 1 2 3 4 5 6 0 1 2 3 4 5 6
time / s time / s
70
60
50
position / m
40
30
20
10
0
0 1 2 3 4 5 6
time / s

169. Motion Graphs
30 10
25 8
acceleration / ms-2
velocity / ms-1
20
6
15
4
10
2
5
0 0
0 1 2 3 4 5 6 0 1 2 3 4 5 6
time / s time / s
70
60
50
position / m
40
30
20
10
0
0 1 2 3 4 5 6
time / s

170. Motion Graphs
30 10
25 8
acceleration / ms-2
velocity / ms-1
20
6
15
4
10
2
5
0 0
0 1 2 3 4 5 6 0 1 2 3 4 5 6
time / s time / s
70
60
50
position / m
40
30
20
10
0
0 1 2 3 4 5 6
time / s

171. Motion Graphs
30 10
25 8
acceleration / ms-2
velocity / ms-1
20
6
15
4
10
2
5
0 0
0 1 2 3 4 5 6 0 1 2 3 4 5 6
time / s time / s
70
60
50
position / m
40
30
20
10
0
0 1 2 3 4 5 6
time / s

172. Motion Graphs
30 10
25 8
acceleration / ms-2
velocity / ms-1
20
6
15
4
10
2
5
0 0
0 1 2 3 4 5 6 0 1 2 3 4 5 6
time / s time / s
70
60
50
position / m
40
30
20
10
0
0 1 2 3 4 5 6
time / s

173. Motion Graphs
30 10
25 8
acceleration / ms-2
velocity / ms-1
20
6
15
4
10
2
5
0 0
0 1 2 3 4 5 6 0 1 2 3 4 5 6
time / s time / s
70
60
50
position / m
40
30
20
10
0
0 1 2 3 4 5 6
time / s

174. Motion Graphs
30 10
25 8
acceleration / ms-2
velocity / ms-1
20
6
15
4
10
2
5
0 0
0 1 2 3 4 5 6 0 1 2 3 4 5 6
time / s time / s
70
60
50
position / m
40
30
20
10
0
0 1 2 3 4 5 6
time / s

175. Acceleration Graphs
10
8
acceleration / ms-2
10 6
9 4
8
2
7
acceleration / ms-2
0
6 0 1 2 3 4 5 6
5 time / s
4
3
2
1
0
0 1 2 3 4 5 6
time / s

176. Acceleration Graphs
10
10
9
8 8
acceleration / ms-2
7
acceleration / ms-2
6 6
5
4
4
3
2
2
1 0
0
0 1 2 3 4 5 6
0 1 2 3 4 5 6
time / s/
time s

177. Acceleration Graphs
10
10
9
8 8
acceleration / ms-2
7
acceleration / ms-2
6 6
5
4
4
3
2
2
1 0
0
0 1 2 3 4 5 6
0 1 2 3 4 5 6
time / s/
time s

178. Acceleration Graphs
10
10
9
8 8
acceleration / ms-2
7
acceleration / ms-2
6 6
5
4
4
3
2
2
1 0
0
0 1 2 3 4 5 6
0 1 2 3 4 5 6
time / s/
time s
Area under the line is the change in velocity

179. Acceleration Graphs
10
10
9
8 8
acceleration / ms-2
7
acceleration / ms-2
6 6
5
4
4
3
2
2 !"#! ! !! ! !!!!! ! !"!!" !! !
1 0
0
0 1 2 3 4 5 6
0 1 2 3 4 5 6
time / s/
time s
Area under the line is the change in velocity