1. Motion
© David Hoult 2009

2. Displacement is distance moved in a specified direction

3. Displacement is distance moved in a specified direction
Displacement is therefore a vector quantity

4. Displacement is distance moved in a specified direction
Displacement is therefore a vector quantity
S I unit of displacement is the meter, m

5. “S I” - système international d'unités… the modern system based on the three fundamental units:
Meter for distance

6. “S I” - système international d'unités… the modern system based on the three fundamental units:
Meter for distance
Second for time

7. “S I” - système international d'unités… the modern system based on the three fundamental units:
Meter for distance
Second for time
Kilogram for mass

8. All other units (for force, electric current, energy etc) are called derived units and are based on the three fundamental units of mass, distance and time.

9. Speed is distance moved per unit time

10. Speed is distance moved per unit time
When stating a speed, no direction needs to be given because speed is a scalar quantity.

11. Speed is distance moved per unit time
When stating a speed, no direction needs to be given because speed is a scalar quantity.
The units of speed are meters per second, ms-1

12. Velocity is distance moved per unit time in a specified direction (and sense)

13. Velocity is distance moved per unit time in a specified direction (and sense)
Velocity is therefore a vector quantity

14. Velocity is distance moved per unit time in a specified direction (and sense)
Velocity is therefore a vector quantity
The units of velocity are meters per second, ms-1

15. Acceleration is the rate of change of velocity

16. Acceleration is the rate of change of velocity
Acceleration is therefore a vector quantity

17. Acceleration is the rate of change of velocity
Acceleration is therefore a vector quantity

18. Acceleration is the rate of change of velocity
Acceleration is therefore a vector quantity

19. Acceleration is the rate of change of velocity
Acceleration is therefore a vector quantity
If the change took 20 seconds and was uniform then the speed (or velocity) changed by

20. Acceleration is the rate of change of velocity
Acceleration is therefore a vector quantity
If the change took 20 seconds and was uniform then the speed (or velocity) changed by
5 meters per second each second

21. The units of acceleration are meters per second per second, ms-2

22. Using Graphs to represent Motion

25. Stationary body

26. Stationary body

28. Body moving with uniform velocity

29. Body moving with uniform velocity

30. Body moving with uniform velocity in the negative sense

31. A B

32. A B
Body B moving faster than body A

33. The slope of a displacement / time graph gives the magnitude and sense of the velocity of the body

34. Body accelerating

35. If the acceleration is uniform the curve is a parabola

36. Body accelerating

37. Body accelerating in the negative sense

40. Uniform velocity

41. Uniform velocity in the negative sense

43. Stationary body

44. Body B moving faster than body A

45. Body B moving faster than body A

46. A B
Body B moving faster than body A

47. Body accelerating uniformly

48. Body accelerating uniformly

49. Body accelerating uniformly in the negative sense

50. The slope of a velocity / time graph gives the magnitude and sense of the acceleration of the body

51. Using a velocity / time graph to find displacement

52. Using a velocity / time graph to find displacement

53. Using a velocity / time graph to find displacement

54. Using a velocity / time graph to find displacement
In 8 seconds, the body moves 10 × 8 = 80 m

55. Using a velocity / time graph to find displacement

56. Using a velocity / time graph to find displacement
The calculation of the displacement of the body is the same as calculating the area under the graph between 0 and 8 seconds

57. The area under a velocity / time graph represents the displacement of the body

58. Equations of Motion

59. These equations are useful when bodies move with uniform acceleration.
Symbols used in the equations:

60. These equations are useful when bodies move with uniform acceleration.
Symbols used in the equations:
t represents time

61. These equations are useful when bodies move with uniform acceleration.
Symbols used in the equations:
t represents time
a represents acceleration

62. These equations are useful when bodies move with uniform acceleration.
Symbols used in the equations:
t represents time
a represents acceleration
u represents “initial” velocity (or speed)

63. These equations are useful when bodies move with uniform acceleration.
Symbols used in the equations:
t represents time
a represents acceleration
u represents “initial” velocity (or speed)
v represents “final” velocity (or speed)

64. These equations are useful when bodies move with uniform acceleration.
Symbols used in the equations:
t represents time
a represents acceleration
u represents “initial” velocity (or speed)
v represents “final” velocity (or speed)
s represents the displacement of the body from a reference point (usually the position of the body at t = 0)

65. The average speed of a body can always be found using

66. The average speed of a body can always be found using

67. If the speed of a body changes from u to v and the acceleration is uniform

68. If the speed of a body changes from u to v and the acceleration is uniform

69. If the speed of a body changes from u to v and the acceleration is uniform

70. If the speed of a body changes from u to v and the acceleration is uniform
In this case the average speed is

71. Therefore, to calculate the displacement of a body at time t, we might use

72. Therefore, to calculate the displacement of a body at time t, we might use
equation 1

73. From the definition of acceleration we have

74. From the definition of acceleration we have
This equation is often rearranged to allow us to find the speed (or velocity) of a body after a period of acceleration

75. From the definition of acceleration we have
This equation is often rearranged to allow us to find the speed (or velocity) of a body after a period of acceleration
v = u + at equation 2

76. Combining equations 1 and 2 in order to eliminate v gives

77. Combining equations 1 and 2 in order to eliminate v gives
s = u t + ½ a t2 equation 3

78. Combining equations 1 and 2 in order to eliminate v gives
s = u t + ½ a t2 equation 3
Combining equations 2 and 3 in order to eliminate t gives

79. Combining equations 1 and 2 in order to eliminate v gives
s = u t + ½ a t2 equation 3
Combining equations 2 and 3 in order to eliminate t gives
v2 = u2 + 2 a s equation 4

80. The Acceleration due to Gravity (g)
(also called Acceleration of Free Fall)

81. The Acceleration due to Gravity (g)
(also called Acceleration of Free Fall)
Experiments show that all bodies fall with the same acceleration

82. The Acceleration due to Gravity (g)
(also called Acceleration of Free Fall)
Experiments show that all bodies fall with the same acceleration as long as air resistance is negligible.

83. The Acceleration due to Gravity (g)
(also called Acceleration of Free Fall)
Experiments show that all bodies fall with the same acceleration as long as air resistance is negligible.
g (in Paris) is about 9.8 ms-2

84. The value of g is not the same at all points on the Earth.

85. The value of g is not the same at all points on the Earth.
The value of g is affected by:

86. The value of g is not the same at all points on the Earth.
The value of g is affected by:
i) altitude

87. The value of g is not the same at all points on the Earth.
The value of g is affected by:
i) altitude

88. The value of g is not the same at all points on the Earth.
The value of g is affected by:
i) altitude
ii) latitude

89. The value of g is not the same at all points on the Earth.
The value of g is affected by:
i) altitude
ii) latitude; the Earth is not a perfect sphere

90. The value of g is not the same at all points on the Earth.
The value of g is affected by:
i) altitude
ii) latitude; the Earth is not a perfect sphere
iii) the rotation of the Earth

91. The value of g is not the same at all points on the Earth.
The value of g is affected by:
i) altitude
ii) latitude; the Earth is not a perfect sphere
iii) the rotation of the Earth
The value of g is less than it would be if the earth did not rotate.

92. The value of g is not the same at all points on the Earth.
The value of g is affected by:
i) altitude
ii) latitude; the Earth is not a perfect sphere
iii) the rotation of the Earth
The value of g is less than it would be if the earth did not rotate.
The value of g is affected most at places where the speed of circular motion is greatest, that is, on the equator