2.2 2.2 ANALYSING MOTION ANALYSING MOTION

GRAPHSGRAPHS

Analying Motion GraphsAnalying Motion Graphs

Data of the motion can be presented in the form of a graph called a motion graph

THE DISPLACEMENT-TIME THE DISPLACEMENT-TIME GRAPHGRAPH

Gradient = change of displacement time

= velocity

S / m

t / sO

A

B

Positive velocity means moving

forward

negative velocity means

moving backward

THE DISPLACEMENT-TIME GRAPHTHE DISPLACEMENT-TIME GRAPH

s / m

t / s

The gradient is positive and

constantMoving forward with a constant

velocityO

A

B

OA

AB The gradient is negative and

constant

Moving backward with a constant

velocity

s / m

t / s

The gradient is zero

zero velocity ie. at rest

THE DISPLACEMENT-TIME GRAPHTHE DISPLACEMENT-TIME GRAPH

Moving forward with a constant velocity and reach the reference

point after 3 s

s / m

t / s3

s / m

t / s

The gradient is positive and increasing

Moving forward with an

acceleration

s / m

t / s

The gradient is positive and decreasing

Moving forward with a deceleration

THE VELOCITY-TIME GRAPHTHE VELOCITY-TIME GRAPH

Gradient = change of velocity time

= acceleration

t / s

V/ m s-1

O

A

B

THE VELOCITY-TIME GRAPHTHE VELOCITY-TIME GRAPH

The gradient is negative and

constantUniform

deceleration

AB

BC The gradient is zero

Zero acceleration i.e. uniform velocity

v / m s-1

t / sO

A

B C

summarysummaryDisplacement-time graph

Velocity-time graph

gradientRepresents velocity

Represents acceleration

Positive gradient

Moves forward

Negative gradient

Moves backward

Zerogradient

stationary

Straight lineUniform velocity Uniform acceleration

acceleration

deceleration

Uniform velocity

Area under graph

No significance Represents distance

Intercept time-axis

Passing through the reference

point

Object stops

evaluationevaluation1. Which of the following graphs shows a body moving with decreasing acceleration ?

Displacement

Time

Displacement

Time

Velocity

Time

Velocity

Time

A

B

C

D

2. Figure below shows the displacement- time graph of a boy. Displacement /m

Time

A

B

C

D

0

The motion of the boy in section AB and BC is

A

B

C

Section AB Section BC

Moving backward at rest

Moving backward uniform velocity

Moving forward at rest

deceleration uniform velocity

3. What information is represented by the gradient and area under a velocity- time graph ?

A

B

C

D

Gradient Area under graph

Acceleration Average velocity

Acceleration displacement

Average velocity displacement

Average velocity acceleration

4. Figure below shows the velocity- time graph of a lorry.

A

B

C

Which of the followings is the correct description of its motion ?

Moving forward with constant velocity , at rest and then moves backward

Accelerates, at rest and then decelerates.Accelerates, moving with constant velocity and then decelerates.

velocity

Time0

A B

C

5. Figure below shows the velocity- time graph of a car.

A

B

C

The acceleration-time graph for the car is

Velocity/m s-

1

Time/s02 3 6

acceleration

time

acceleration

time

acceleration

timeacceleratio

n

time

D

To determine To determine displacement, velocity displacement, velocity and acceleration from and acceleration from

motion graphmotion graph

Example

The graph shows the motion of a moving particle.

(a) What is the displacement of the particle from the starting point

just before it moves with a uniform velocity.

(b) Calculate the velocity of the particle in the first 20 s.

O0 10 20 30 40 50 60

Time / s

20

40

60

80

100

Displacement /m

A

B

(c) Calculate the average velocity

40 m

Velocity = gradient AB

Average Velocity = displacement time

= 80 + (-60) = 0.333 m s-1

60

= (100 – 20)m 20 s

= 4 m s-1

S1 = 80 m, S2 = -60m, S3= 0 m

Example

The graph shows the motion of a moving particle.

(a) What is the velocity of the particle from t=30 s to t= 60 s ?

(b) Calculate the average velocity(c) Calculate the

average speed

Velocity = gradient (c) Average speed = total distance time

= 25+ 15 = 0.667 m s-1 60

010 20 30 40 50 60

Time / s

-5

5

10

15

Displacement /m

B

-10(b) Average Velocity = displacement time

= (-25 )+15 = -0.167 m s-1 60

(30,-10)(60, 5)= 5-(-10) m

(60-30) s= 0.5 m s-1

S1 = -10-15 = -25 m

S2 = 5 –(-10) = 15m

Example

The graph shows the motion of a motorcycle.

(a) Calculate the deceleration of the motorcycle.

(b) Calculate the average velocity of the motorcycle.

velocity/m s-1

Deceleration = gradient CD = 20 - 0 m s-1

40 – 60 s

= -1 m s-2

Average Velocity = Displacement time

(40, 20)

(60, 0)

0 10 20 30 40 50 60

Time / s

5

10

15

20

A B

DS1

C

S3S2

S1= (10)(10) = 100 m

S2= 1 (10+ 20)30 = 450m 2S3= 1 (20)(20) = 200m 2

= 100 + 450 + 200 60= 12.5 ms-1

S2

S1

Example

The graph shows the motion of a motorcycle.

(a) Calculate the average velocity of the motorcycle

(b) Calculate the average speed of the motorcycle.

= 150 + 150 + 25 m 60 s= 5.417 ms-1

(a) Average Velocity = Displacement time

S1= ½ (20)(15) =150 mvelocity/m s-1

010 20 30 40 50 60

Time / s

-5

5

10

15

-10

S3

S2= ½ (30)(-10) =-150 mS3= ½ (10)(5) 25 m

= 150 + (-150)+ 25 m 60 s= 0.417 m s-1

(b) Average speed = Total distance time

SummarySummaryDisplacement-time graphDisplacement-time graph determine velocity from the gradientdetermine velocity from the gradient area under graph = no significancearea under graph = no significance

Velociity -time graphVelociity -time graph determine acceleration from the determine acceleration from the

gradientgradient determine displacement from the determine displacement from the

area area under graph under graphAverage velocity = displacement / timeAverage velocity = displacement / time

Average speed = distance / timeAverage speed = distance / time