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# Kinematics

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Speed, Velocity & Acceleration …

Speed, Velocity & Acceleration
Graphical Analysis of Motion
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• 1. Speed, velocity and acceleration Graphical analysis of motion Free-fall Kinematics 1
• 2. Kinematics 2
• 3. ο Distance is the total length travel irrespective of the direction of motion. It is a scalar quantity. ο Displacement is the distance moved in a particular direction. It is a vector quantity. Kinematics 3
• 4. Kinematics 4 Actual length covered by moving body irrespective the direction Shortest distance between initial and final position
• 5. Aspect Distance Displacement Definition Total route by a motion Distance taken with consideration of direction Type of quantity Scalar quantity Vector quantity SI Unit metre / m Kinematics 5
• 6. ο If you walk 2 km from home to school, and 2 km back to school to home, then you have travelled a total distance of 4 km. On the other hand, as your final position is the same as your initial position, your displacement is zero. ο A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. ο’ What is the total distance travelled? ο’ What is the boyβs displacement from P? Kinematics 6
• 7. Kinematics 7
• 8. ο The speed of an object is the distance moved by the object per unit time. It also is defined as the rate of change of distance. ο The common units for speed are metres per second (m s-1) and kilometres per hour ( km h-1). Kinematics 8 TakenTime travelledDistance Speed ο½ t d v ο½
• 9. ο For most journeys, speed is not constant. Normally we take the journey as a whole and calculate the average speed. ο This average speed is also known as the instantaneous speed. ο Example 2 ο‘ If a car is taken from the garage, driven for 100 km before returning to the garage after 2 hours, what is it average speed? Kinematics 9 takentimeTotal travelleddistanceTotal speedAverage ο½
• 10. ο Velocity is the distance travelled per unit time in a specified direction. It is also defined as the rate of change of displacement. ο Velocity is also measured in m s-1 and km h-1. ο It is a vector quantity as the direction of travel is important. Kinematics 10
• 11. Aspect Speed Velocity Definition Rate of change of distance Rate of change of displacement Type of Quantity Scalar Vector Formula Speed = Total distance Time Velocity = Total displacement time SI Unit metre per second / m s-1 Kinematics 11
• 12. ο Example 3 ο‘ A cyclist travels 6 km due east and then makes a turn to travel a further distance of 8 km due north. The whole journey takes 2 hours. Calculate ο’ the distance travelled by the cyclist, ο’ the average speed of the cyclist, ο’ the displacement of the cyclist, ο’ the average velocity of the cyclist. Kinematics 12
• 13. ο Example 4 ο‘ A boy run 5 km due west and then return back to travel a further distance of 4 km before resting. The whole journey takes 1 hour. Calculate ο’ his total distance travelled, ο’ his average speed, ο’ his displacement from the starting point, ο’ his average velocity. Kinematics 13
• 14. ο Example 5 ο‘ A car starts from point O and moves to U, 50 m to the north in 60 s. The car then moves to B, 120 m to the west in 40 s. Finally, it stops. Calculate the: ο’ total distance moved by the car ο’ displacement of the car ο’ speed of the car when it is moves to the north ο’ velocity of the car ο’ average speed of the car Kinematics 14
• 15. 1. A car travels along the route PQRST in 30 minutes. What is the average speed of the car? A. 10 km / hour B. 20 km / hour C. 30 km / hour D. 60 km / hour Kinematics 15
• 16. 2. A man crosses a road 8.0 m wide at a speed of 2.0 m / s. How long does the man take to cross the road? A. 4.0 s B. 6.0 s C. 10 s D. 16 s Kinematics 16
• 17. 3. A child is standing on the platform of a station, watching the trains. A train travelling at 30 m / s takes 3 s to pass the child. What is the length of the train? A. 10 m B. 30 m C. 90 m D. 270 m Kinematics 17
• 18. 4. A car driver takes a total of two hours to make a journey of 75 km. She has a coffee break of half an hour and spends a quarter of an hour stationary in a traffic jam. At what average speed must she travel during the rest of the time if she wants to complete the journey in the two hours? 1. 38 km/ h 2. 50 km/ h 3. 60 km/ h 4. 75 km/ h Kinematics 18
• 19. 5. A car takes 1 hour to travel 100 km along a main road and then Β½ hour to travel 20 km along a side road. What is the average speed of the car for the whole journey? A. 60 km / h B. 70 km / h C. 80 km / h D. 100 km / h Kinematics 19
• 20. 6. A car travels at various speeds during a short journey. 7. The table shows the distances travelled and the time taken during each of four stages P, Q, R and S. Kinematics 20
• 21. 1. During which two stages is the car travelling at the same speed? A. P and Q B. P and S C. Q and R D. R and S Kinematics 21
• 22. 7. A train travels along a track from Aytown to Beetown. The map shows the route. Kinematics 22
• 23. 1. The distance travelled by the train between the towns is 210 km. It moves at an average speed of 70 km/ h. 2. How long does the journey take? Kinematics 23
• 24. 8. The circuit of a motor racing track is 3 km in length. In a race, a car goes 25 times round the circuit in 30 minutes. 9. What is the average speed of the car? A. 75 km / hour B. 90 km / hour C. 150 km / hour D. 750 km / hour Kinematics 24
• 25. 9. A tunnel has a length of 50 km. A car takes 20 min to travel between the two ends of the tunnel. 10. What is the average speed of the car? A. 2.5 km/ h B. 16.6 km/ h C. 150 km/ h D. 1000 km/ h Kinematics 25
• 26. Kinematics 26
• 27. ο Acceleration is defined as the rate of change of velocity. ο The SI unit for acceleration is m s-2. ο Acceleration is a vector quantity. The direction of acceleration is the direction of change in velocity. Kinematics 27 takenTime yin velocitChange onAccelerati ο½ t uv a ο­ ο½
• 28. ο There is acceleration only when velocity changes. ο‘ If velocity is constant throughout, there is no acceleration. ο‘ If the velocity is increasing, the object is said to be accelerating. ο‘ If the velocity is decreasing, then the object is said to have negative acceleration or deceleration or retardation. οA body is said to move with uniform acceleration if its rate of change of velocity with time is constant. Kinematics 28
• 29. 1. A car accelerates from rest to 50 ms-1 in 10 s. Calculates the acceleration of the car. 2. A car is uniformly retarded and brought to rest from a speed of 108 ms-1 in 15 s. Find its acceleration. 3. The driver of a car brakes when the car is travelling at 30 ms-1. The velocity of the car is reduced to 10 ms-1 after 5 s. What is its average acceleration? Kinematics 29
• 30. 4. If a car can accelerate at 3.2 ms-2, how long will it take to speed up from 15 ms-1 to 22 ms-1? 5. How fast does a motorcycle travel if it starts at rest and is going 22 ms-1 after 5 seconds? 6. What is the acceleration of a car that speeds up from 12 ms-1 to 30 ms-1 in 15 seconds? 7. A truck travelling at 25 ms-1 puts its brakes on for 4 s. This produces a retardation of 2 ms-2. What does the truckβs velocity drop to? Kinematics 30
• 31. 8. How fast does a car travel if it is going 4 m/s and accelerates at 3.5 m/s2 for 5 seconds? 9. If a car is going at 12 m/s, how long will it take to reach a speed of 26 m/s if it accelerates at 2.2 m/s2? 10. A car moving along a straight level road has an initial speed of 3 m/s and its acceleration is 2 m/s2. What is the speed of the car after 5 s? Kinematics 31
• 32. 11. A car sets off from a traffic lights. It reaches a speed of 27 m/s in 18 s. What is its acceleration? 12. A train, initially moving at 12 m/s, speeds up to 36 m/s in 120 s. What is its acceleration? Kinematics 32
• 33. Kinematics 33
• 34. ο A common way of analyzing the motion of objects in physics labs is to perform a ticker tape analysis. Kinematics 34
• 35. ο A ticker tape timer consists of an electrical vibrator which vibrates 50 times per second. ο The time interval between two adjacent dots on the ticker-tape is called one tick. ο One tick is equal to 1/50 s or 0.02 s. Kinematics 35
• 36. 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
• 37. ο The trail of dots provides a history of the object's motion and is therefore a representation of the object's motion. ο The distance between dots on a ticker tape represents the object's position change during that time interval. ο‘ A large distance between dots indicates that the object was moving fast during that time interval. ο‘ A small distance between dots means the object was moving slow during that time interval. Kinematics 37
• 38. 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
• 39. ο 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
• 40. 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.
• 41. Kinematics 41
• 42. ο Gradient = 0 Hence, velocity = 0 Kinematics 43
• 43. ο Gradient is constant, Hence, velocity is uniform Kinematics 45
• 44. ο Gradient is increasing ο Hence velocity is increasing. Kinematics 47
• 45. ο Gradient is decreasing ο Hence velocity is decreasing. Kinematics 48
• 46. Kinematics 49 y-axis x-axis ππππππππ‘ = πβππππ ππ π¦ β ππ₯ππ  πβππππ ππ π₯ β ππ₯ππ  ππππππππ‘ = πππ πππππππππ‘ π‘πππ ππππππππ‘ = π£ππππππ‘π¦ ππ ππππππ‘ βπ¦ βπ₯
• 47. Kinematics 50
• 48. Kinematics 52
• 49. Kinematics 54
• 50. Kinematics 56
• 51. Kinematics 57
• 52. ο Increasing acceleration Kinematics 58
• 53. ο Decreasing acceleration Kinematics 59
• 54. Kinematics 60 ππππππππ‘ = πβππππ ππ π¦ β ππ₯ππ  πβππππ ππ π₯ β ππ₯ππ  ππππππππ‘ = π£ππππππ‘π¦ π‘πππ x-axis y-axis ππππππππ‘ = πππππππππ‘πππ ππ ππππππ‘ βπ¦ βπ₯
• 55. Kinematics 61 π΄πππ ππ ππππ‘πππππ = ππππ‘β Γ πΏππππ‘β π΄πππ ππ ππππ‘πππππ = πππππππ‘π¦ Γ ππππ width length πππππππ‘π¦ Γ ππππ = π·ππ πππππππππ‘ π΄πππ π’ππππ π‘βπ ππππβ = π·ππ πππππππππ‘
• 56. ο From the displacement-time graph ο‘ Its gradient gives the velocity of the moving object. ο From velocity-time graph ο‘ Its gradient gives the acceleration of the moving object. ο‘ The area under the graph gives the distance travelled by the object Kinematics 62
• 57. 5 10 15 30 60 90 120 velocity(m/s) time(s) goingupthehill waitingat trafficlights Kinematics 63 Figure below shows the velocity a cyclist as she cycled through a town.
• 58. 1. What was the cyclistβ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
• 59. ο 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
• 60. 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
• 61. ο 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 Velocity(m/s) Time(s)
• 62. 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
• 63. ο 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
• 64. Kinematics 70 10 velocity (m/s) time (s) 5 20 30
• 65. πππππππππ‘πππ = ππππππππ‘ ππ ππππβ = π¦2 β π¦1 π₯2 β π₯1 πππππππππ‘πππ = 10 β 0 20 β 30 πππππππππ‘πππ = 10 β10 = β1 π/π 2 Kinematics 71
• 66. π‘ππ‘ππ πππ π‘ππππ π‘πππ£πππππ = ππππ π’ππππ ππππβ πππ π‘ππππ π‘πππ£πππππ = 1 2 (15 + 30)(10) πππ π‘ππππ π‘πππ£πππππ = 1 2 (45)(10) = 225 π Kinematics 72
• 67. ο 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. ο‘ It started from rest and gain a speed of 40 ms-1 in 2 s. ο‘ It then travel with this speed constantly for 10 s. ο‘ Finally it decelerates and reach the other station within 2 s. Kinematics 73
• 68. ο 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
• 69. Kinematics 75 40 velocity (m/s) time (s) 2 12 14
• 70. πππππππππ‘πππ = ππππππππ‘ ππ ππππβ = π¦2 β π¦1 π₯2 β π₯1 πππππππππ‘πππ = 40 β 0 2 β 0 πππππππππ‘πππ = 40 2 = 20 π/π 2 Kinematics 76
• 71. π‘ππ‘ππ πππ π‘ππππ π‘πππ£πππππ = ππππ π’ππππ ππππβ πππ π‘ππππ π‘πππ£πππππ = 1 2 (14 + 10)(40) πππ π‘ππππ π‘πππ£πππππ = 1 2 (24)(40) = 480 π Kinematics 77
• 72. ππ£πππππ π£ππππππ‘π¦ = π‘ππ‘ππ πππ π‘ππππ π‘πππ£ππππ π‘ππ‘ππ π‘πππ π‘ππππ ππ£πππππ π£ππππππ‘π¦ = 480 14 ππ£πππππ π£ππππππ‘π¦ = 34.3 π/π  Kinematics 78
• 73. 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
• 74. 2. Which of the following defines acceleration? Kinematics 80 A
• 75. 3. Which quantity X is calculated using this equation? A. acceleration B. average velocity C. distance travelled D. speed Kinematics 81
• 76. 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
• 77. 5. A tennis player hits a ball over the net. Kinematics 83
• 78. 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
• 79. 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
• 80. 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
• 81. 7. Which speed / time graph applies to an object at rest? Kinematics 87 D
• 82. 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
• 83. 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
• 84. Kinematics 90 C
• 85. 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
• 86. 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
• 87. 11. The diagram shows a speed-time graph for a body moving with constant acceleration. Kinematics 93
• 88. 1. What is represented by the shaded area under the graph? A. acceleration B. distance C. speed D. time Kinematics 94
• 89. 12. The graph illustrates the motion of an object. Kinematics 95
• 90. 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
• 91. 13. A cyclist is riding along a road when an animal runs in front of him. The graph shows the cyclistβs motion. He sees the animal at P, starts to brake at Q and stops at R. Kinematics 97
• 92. 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
• 93. 14. The diagram shows the speed-time graph for an object moving at constant speed. Kinematics 99
• 94. 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
• 95. 15. A car accelerates from traffic lights. The graph shows how the carβs speed changes with time. Kinematics 101
• 96. 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
• 97. 16. The graph represents the movement of a body accelerating from rest. Kinematics 103
• 98. 1. After 5 seconds how far has the body moved? A. 2 m B. 10 m C. 25 m D. 50 m Kinematics 104
• 99. 17. The graph shows the movement of a car over a period of 50 s. Kinematics 105
• 100. 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
• 101. 18. The graph shows the movement of a car over a period of 50 s. Kinematics 107
• 102. 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
• 103. 19. The graph represents part of the journey of a car. Kinematics 109
• 104. 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
• 105. Kinematics 111
• 106. Kinematics 112
• 107. Kinematics 113
• 108. Kinematics 114
• 109. Kinematics 115
• 110. Kinematics 116
• 111. Kinematics 117
• 112. ο A free falling object is an object that is falling under the sole influence of gravity. ο 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
• 113. ο There are three important motion characteristics that are true of free- falling objects: ο‘ Free-falling objects do not encounter air resistance. ο‘ All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s2 (often approximated as 10 m/s2) ο‘ Not affected by mass and shape of the object. Kinematics 119
• 114. Kinematics 120 Velocity Time
• 115. Kinematics 121 At the start of his jump the air resistance is zero so he accelerate downwards.
• 116. Kinematics 122 As his speed increases his air resistance will also increase
• 117. Kinematics 123 Eventually the air resistance will be big enough to balance the skydiverβs weight.
• 118. How the forces change with time. KEY Gravity (constant value & always presentβ¦weight) Air resistance (friction) Net force (acceleration OR changing velocity)
• 119. ο The size of the air resistance on an object depends on the area of the object and its speed; ο‘ the larger the area, the larger the air resistance. ο‘ the faster the speed, the larger the air resistance. Kinematics 125
• 120. Kinematics 126 When he opens his parachute the air resistance suddenly increases, causing him to start slow down.
• 121. 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.
• 122. Velocity Time Speed increasesβ¦ Terminal velocity reachedβ¦ Parachute opens β diver slows down New, lower terminal velocity reached Diver hits the ground
• 123. 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
• 124. 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
• 125. 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
• 126. 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
• 127. 5. Which graph shows the motion of a heavy, steel ball falling from a height of 2 m? Kinematics 133 A
• 128. 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
• 129. 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
• 130. 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
• 131. 9. Which graph represents the motion of a body falling vertically that reaches a terminal velocity? Kinematics 137 B
• 132. 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
• 133. (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
• 134. (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
• 135. (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 β 0 4 acceleration = 10 m/s2 (c) distance = area under the graph distance = 1 2 Γ 40 Γ 4 distance = 80 m
• 136. LEARNING OUTCOMES Kinematics 142
• 137. ο State what is meant by speed and velocity. ο Calculate average speed using distance travelled/time taken. ο State what is meant by uniform acceleration and calculate the value of an acceleration using change in velocity/time taken. ο Discuss non-uniform acceleration. Kinematics 143
• 138. ο Plot and interpret speed-time and distance- time graphs. ο Recognise from the shape of a speed-time graph when a body is ο‘ at rest, ο‘ moving with uniform speed, ο‘ moving with uniform acceleration, ο‘ moving with non-uniform acceleration. ο Calculate the area under a speed-time graph to determine the distance travelled for motion with uniform speed or uniform acceleration. Kinematics 144
• 139. ο State that the acceleration of free-fall for a body near to the Earth is constant and is approximately 10 m/s2. ο Describe qualitatively the motion of bodies with constant weight falling with and without air resistance (including reference to terminal velocity). Kinematics 145