KINEMATICS

Speed, velocity and acceleration

Graphical analysis of motionFree-fall

Kinematics 1

DISTANCE & DISPLACEMENT

Kinematics 2

DISTANCE & DISPLACEMENT Distance is the total length travel

irrespective of the direction of motion. It is a scalar quantity.

Displacement is the distance moved in a particular direction. It is a vector quantity.

Kinematics 3

Kinematics 4

Actual length covered by moving body irrespective the direction

Shortest distance between initial and final position

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

DISPLACEMENT EXAMPLE 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.

A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.

What is the total distance travelled? What is the boy’s displacement from P?

Kinematics 6

SPEED & VELOCITY

Kinematics 7

SPEED & VELOCITY 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.

The common units for speed are metres per second (m s-1) and kilometres per hour ( km h-1).

Kinematics 8

Taken Timetravelled Distance

Speed

td

v

For most journeys, speed is not constant. Normally we take the journey as a whole and calculate the average speed.

This average speed is also known as the instantaneous speed.

Example 2 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

taken timeTotal

travelleddistance Totalspeed Average

Velocity is the distance travelled per unit time in a specified direction. It is also defined as the rate of change of displacement.

Velocity is also measured in m s-1 and km h-1.

It is a vector quantity as the direction of travel is important.

Kinematics 10

Aspect Speed Velocity

Definition Rate of change of distance

Rate of change of displacement

Type of Quantity Scalar Vector

FormulaSpeed = Total distance Time

Velocity = Total displacement

time

SI Unit metre per second / m s-1

Kinematics 11

Example 3A 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 the distance travelled by the cyclist,the average speed of the cyclist,the displacement of the cyclist,the average velocity of the cyclist.

Kinematics 12

Example 4A 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 his total distance travelled, his average speed, his displacement from the starting point, his average velocity.

Kinematics 13

Example 5A 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: total distance moved by the car displacement of the car speed of the car when it is moves to the north velocity of the car average speed of the car

Kinematics 14

EXAMPLE1. A car travels along the route PQRST in 30

minutes.

What is the average speed of the car?A. 10 km / hourB. 20 km / hourC. 30 km / hourD. 60 km / hour

Kinematics 15

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

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 mC. 90 m D. 270 m

Kinematics 17

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/ h2. 50 km/ h3. 60 km/ h4. 75 km/ h Kinematics 18

5. A car takes 1 hour to travel 100 km along a main road and then ½ hour to travel 20 km along a side road.

What is the average speed of the car

for the whole journey?A. 60 km / hB. 70 km / hC. 80 km / hD. 100 km / h

Kinematics 19

0625/01/O/N/08 Q36. 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

1. During which two stages is the car travelling at the same speed?

A. P and QB. P and SC. Q and RD. R and S

Kinematics 21

0625/01/O/N/03 Q47. A train travels along a track from

Aytown to Beetown. The map shows the route.

Kinematics 22

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

0625/01/M/J/08 Q38. 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 / hourB. 90 km / hourC. 150 km / hourD. 750 km / hour

Kinematics 24

0625/01/M/J/03 Q49. 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/ hB. 16.6 km/ hC. 150 km/ hD. 1000 km/ h

Kinematics 25

ACCELERATION

Kinematics 26

ACCELERATION Acceleration is defined as the rate of

change of velocity.

The SI unit for acceleration is m s-2. Acceleration is a vector quantity. The

direction of acceleration is the direction of change in velocity.

Kinematics 27

takenTime

yin velocit Change on Accelerati

tuv

a

There is acceleration only when velocity changes. If velocity is constant throughout,

there is no acceleration.If the velocity is increasing, the object

is said to be accelerating. If the velocity is decreasing, then the

object is said to have negative acceleration or deceleration or retardation.

A body is said to move with uniform acceleration if its rate of change of velocity with time is constant.

Kinematics 28

EXAMPLE1. A car accelerates from rest to 50

ms-1 in 10 s. Calculate 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

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 truck’s velocity drop to?

Kinematics 30

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

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

TICKER TAPE DIAGRAMS

Kinematics 33

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

Kinematics 34

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

EXAMPLEFind 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

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

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

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

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.

DISPLACEMENT-TIME GRAPH

Kinematics 41

AT REST

Gradient = 0Hence, velocity = 0

Kinematics 43

UNIFORM VELOCITY

Gradient is constant,Hence, velocity is uniform

Kinematics 45

ACCELERATION

Gradient is increasing Hence velocity is increasing.

Kinematics 47

DECELERATION

Gradient is decreasing Hence velocity is decreasing.

Kinematics 48

GRADIENT OF DISPLACEMENT-TIME GRAPH

Kinematics 49

y-a

xis

x-axis

𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡=h𝑐 𝑎𝑛𝑔𝑒𝑖𝑛𝑦−𝑎𝑥𝑖𝑠h𝑐 𝑎𝑛𝑔𝑒𝑖𝑛𝑥−𝑎𝑥𝑖𝑠

𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡=𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡

𝑡𝑖𝑚𝑒

𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡=𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑜𝑏𝑗𝑒𝑐𝑡

∆ 𝑦

∆ 𝑥

VELOCITY-TIME GRAPH

Kinematics 50

AT REST

Kinematics 52

UNIFORM VELOCITY

Kinematics 54

UNIFORM ACCELERATION

Kinematics 56

UNIFORM DECELERATION

Kinematics 57

NON-UNIFORM ACCELERATION

Increasing acceleration

Kinematics 58

NON- UNIFORM DECELERATION

Decreasing acceleration

Kinematics 59

GRADIENT OF VELOCITY-TIME GRAPH

Kinematics 60

𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡=h𝑐 𝑎𝑛𝑔𝑒𝑖𝑛𝑦−𝑎𝑥𝑖𝑠h𝑐 𝑎𝑛𝑔𝑒𝑖𝑛𝑥−𝑎𝑥𝑖𝑠

𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡=𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦𝑡𝑖𝑚𝑒

x-axis

y-a

xis

𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡=𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑜𝑓 𝑜𝑏𝑗𝑒𝑐𝑡∆ 𝑦

∆ 𝑥

AREA UNDER THE GRAPH OF VELOCITY-TIME GRAPH

Kinematics 61

𝐴𝑟𝑒𝑎𝑜𝑓 𝑅𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒= h𝑊𝑖𝑑𝑡 × h𝐿𝑒𝑛𝑔𝑡

𝐴𝑟𝑒𝑎𝑜𝑓 𝑅𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒=𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦×𝑇𝑖𝑚𝑒

wid

th

length

𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦×𝑇𝑖𝑚𝑒=𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡

𝐴𝑟𝑒𝑎𝑢𝑛𝑑𝑒𝑟 h𝑡 𝑒 h𝑔𝑟𝑎𝑝 =𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡

INTERPRETING GRAPH 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

EXAMPLE 1

5

10

15

30 60 90 120

velo

city

(m

/s)

time (s)

going up the hill

waiting at traffic lights

Kinematics 63

Figure below shows the velocity a cyclist as she cycled through a town.

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

EXAMPLE 2 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

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

EXAMPLE 3 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

Velo

city (

m/s

)

Time (s)

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

EXAMPLE 4 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

Kinematics 70

10

velocity (m/s)

time (s)5 20 30

Kinematics 71

Kinematics 72

EXAMPLE 5 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

EXAMPLE 5 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

Kinematics 75

40

velocity (m/s)

time (s)2 12 14

Kinematics 76

Kinematics 77

Kinematics 78

1. What must change when a body is accelerating?

A. the force acting on the bodyB. the mass of the bodyC. the speed of the bodyD. the velocity of the body

Kinematics 79

2. Which of the following defines acceleration?

Kinematics 80

A

3. Which quantity X is calculated using this equation?

A. accelerationB. average velocityC. distance travelledD. speed

Kinematics 81

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

5. A tennis player hits a ball over the net.

Kinematics 83

1. In which position is the ball accelerating?

A. P and Q onlyB. P and R onlyC. Q and R onlyD. P, Q and R

Kinematics 84

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

1. What was the speed of the object?A. 2.0 cm / sB. 5.0 cm / sC. 100 cm / sD. 200 cm / s

Kinematics 86

7. Which speed / time graph applies to an object at rest?

Kinematics 87

D

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

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

Kinematics 90

C

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

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

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

Kinematics 93

1. What is represented by the shaded area under the graph?

A. accelerationB. distanceC. speedD. time

Kinematics 94

12. The graph illustrates the motion of an object.

Kinematics 95

1. Which feature of the graph represents the distance travelled by the object whilst moving at a constant speed?

A. area SB. area S + area TC. area TD. the gradient at point X

Kinematics 96

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

1. What is used to find the distance travelled after he applies the brakes?

A. the area under line PQB. the area under line QRC. the gradient of line PQD. the gradient of line QR

Kinematics 98

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

Kinematics 99

1. What is the distance travelled by the object in the first 3 s?

A. 1.5 mB. 2.0 mC. 3.0 mD. 6.0 m

Kinematics 100

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

Kinematics 101

1. How far does the car travel before it reaches a steady speed?

A. 10 mB. 20 mC. 100 mD. 200 m

Kinematics 102

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

Kinematics 103

1. After 5 seconds how far has the body moved?

A. 2 mB. 10 mC. 25 mD. 50 m

Kinematics 104

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

Kinematics 105

1. What was the distance travelled by the car during the time when it was moving at a steady speed?

A. 10 mB. 100 mC. 200 mD. 400 m

Kinematics 106

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

Kinematics 107

1. What was the distance travelled by the car while its speed was increasing?

A. 10 mB. 20 mC. 100 mD. 200 m

Kinematics 108

19. The graph represents part of the journey of a car.

Kinematics 109

1. What distance does the car travel during this part of the journey?

A. 150 mB. 300 mC. 600 mD. 1200 m

Kinematics 110

QUESTION 1

Kinematics 111

QUESTION 2

Kinematics 112

QUESTION 3

Kinematics 113

QUESTION 4

Kinematics 114

QUESTION 5

Kinematics 115

QUESTION 6

Kinematics 116

FREE FALL

Kinematics 117

FALLING FREELY 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

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

Kinematics 120

Velocity

Time

SKYDIVING

Kinematics 121

At the start of his jump the air resistance is zero

so he accelerate downwards.

SKYDIVING

Kinematics 122

As his speed increases his air resistance will also

increase

SKYDIVING

Kinematics 123

Eventually the air resistance will be big enough to balance the

skydiver’s weight.

How the forces change with time.

KEY Gravity

(constant value & always present…weight)

Air resistance

(friction)

Net force(acceleration OR changing

velocity)

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

SKYDIVING

Kinematics 126

When he opens his parachute the air

resistance suddenly increases,

causing him to start slow down.

SKYDIVING

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.

VELOCITY-TIME GRAPH FOR THE SKY DIVER

Velo

cit

y

Time

Speed increases…

Terminal velocity reached…

Parachute opens – diver slows down

New, lower terminal velocity reached

Diver hits the ground

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

2. A student drops a table-tennis ball in air.

3. What happens to the velocity and to the acceleration of the ball during the first few seconds after release?

Kinematics 130

C

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

4. The three balls shown are dropped from a bench.

Which balls have the same acceleration?

A. aluminium and lead onlyB. aluminium and wood onlyC. lead and wood onlyD. aluminium, lead and wood

Kinematics 132

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

Kinematics 133

A

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

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

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

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

Kinematics 137

B

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

QUESTION 1(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 gravityor air resistance increases as speed increases

(iii) air resistance = weightor downward force balances upward forceor no resultant force

QUESTION 2

(a) (i) 9.8 m/s2 or 10 m/s2

Kinematics 140

(b)

(i) air resistance = weightor downward force balances upward forceor no resultant force

(ii) weight larger than air resistanceor downward force greater than upward force

(c) coin and paper accelerate at 10 m/s2

hit bottom at the same timenot fall at same time

QUESTION 3

(a) decelerating uniformly and comes to rest at 4 s

Kinematics 141

(b)

(i) 40 m/s

(ii) 4 s(c)

acceleration = 10 m/s2

(c)

distance = 80 m

KINEMATICSLEARNING OUTCOMES

Kinematics 142

SPEED, VELOCITY & ACCELERATION 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

GRAPHICAL ANALYSIS OF MOTION Plot and interpret speed-time and

distance-time graphs. Recognise from the shape of a speed-

time graph when a body isat 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

FREE-FALL 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