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1 11Equation Chapter (Next) Section 1 Analysing Motion Graph Learning outcomes 1. plot and interpret displacement - time and velocity time graph 2. deduce from the shape of a displacement - time graph when a body is (a) at rest (b) moving with uniform velocity (c) moving with non-uniform velocity 3. determine distance, displacement and velocity from a displacement - time graph 4. deduce from the shape of a velocity - time graph when a body is (a) at rest (b) moving with uniform velocity (c) moving with uniform acceleration 5. determine distance, displacement, velocity and acceleration from a velocity - time graph 6. Solve problems on linear motion with uniform acceleration Displacement - time graph 1. A displacement-time graph (s - t graph) is a graph showing (a) the position of an object from its original position changes with time (b) the displacement of the object changes with time 2. The gradient of a displacement - time graph gives the velocity. Displacem ent - time graph Position and The object is rest over a period of The object moves in the original The object moves in the original Lesson 3 A
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Page 1: Lesson 3

111EquationChapter (Next) Section 1

Analysing Motion Graph

Learning outcomes1. plot and interpret displacement - time and velocity time graph2. deduce from the shape of a displacement - time graph when a body is

(a) at rest(b) moving with uniform velocity(c) moving with non-uniform velocity

3. determine distance, displacement and velocity from a displacement - time graph4. deduce from the shape of a velocity - time graph when a body is

(a) at rest(b) moving with uniform velocity(c) moving with uniform acceleration

5. determine distance, displacement, velocity and acceleration from a velocity - time graph6. Solve problems on linear motion with uniform acceleration

Displacement - time graph

1. A displacement-time graph (s - t graph) is a graph showing(a) the position of an object from its original position changes with time(b) the displacement of the object changes with time

2. The gradient of a displacement - time graph gives the velocity.

Displacement - time graph

Position and movement of

object

The object is rest over a period of time

It is x m from its original position in the original direction

The object moves in the original direction from its original position

The object moves in the original direction from its original position

DisplacementDisplacement is constant Displacement increasing

uniformlyDisplacement is increasing non uniformly

Velocity

gradient = zerovelocity = zero

gradient = positive and constantvelocity = positive and constant

gradient = increasing and positivevelocity = increasing and positive

Lesson 3

A

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Velocity - time graph

1. A velocity-time graph (s - t graph) is a graph showing how the velocity of an object changes with time.

2. The gradient of a velocity - time graph gives the acceleration.3. The area under the graph of a velocity - time graph gives the displacement (or distance

travelled)

Velocity - time graph

VelocityIts velocity is constant over a period of time

Its velocity increases linearly (at constant rate)

Its velocity decreases linearly( at constant rate)

Acceleration

The gradient of graph is zero.Hence, its acceleration is zero.

The gradient of graph is positive and constant.

Hence, the object experiences constant acceleration

The gradient of graph is negative and constant

Hence, the object experiences constant deceleration

Compare displacement-time graph and velocity-time graph

Displacement-time graph Velocity-time graph

AB: Constant positive gradientBC: Zero gradientCD: Constant negative gradient

gradient of graphAB: Constant positive gradientBC: Zero gradientCD: Constant negative gradient

AB: Moves in the original directionBC: Stationary( at rest)CD: Moves in the opposite direction

position and movementAt regions AB, BC, and CD, the object is moving in the positive direction.

AB: constant positive velocityBC: zero velocityCD: constant negative velocity

velocity of objectAB: Velocity increasing linearlyBC: Constant velocityCD: velocity decreasing linearly

At regions AB, BC and CD the object experiences zero acceleration. acceleration of object

AB: Constant accelerationBC: Zero accelerationCD: Constant deceleration

No physical meaningarea under graph

The area under the graph refers to the displacement of the object

Summary1. Gradient of the graph of displacement against time gives the _________ of an object.

B

C

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2. Gradient of the graph of velocity against time gives the __________ of an object.3. Area under the graph of velocity against time gives the __________ travelled by the object

Page 4: Lesson 3

Try it yourself

1. Using your own words, describe the motion of the particle represented by the flowing displacement-time graph.

(a)

(b)

(c)

(d)

(e)

(f)

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2. Using your own words, describe the motions of a particle represented by the following velocity-time graph.

(a)

(b)

(c)

(d)

(e)

(f)

Page 6: Lesson 3

3. Diagram 1 shows a displacement-time graph of a particle.(a) What is the displacement of the particle after 10 s?(b) Calculate average velocity of the particle in the time

interval(i) from t = 4 s to t = 8 s(ii) from t = 8 s to t =10 s

(c) Calculate the average speed for the whole journey

4. The graph in Diagram 2 shows the displacement-time graph of a roller skater.Calculate(a) the maximum velocity of the skater(b) the velocity of the skater when he returns to his original

position(c) the displacement of the skater when t = 50 s(d) the average velocity throughout the whole journey(e) average speed throughout the whole journey

5. Diagram 3 shows a velocity-time graph.

Diagram 3

Find(a) its acceleration(b) the distance travelled in the time interval from t = 2 s to t = 6 s.

6. A stone is being thrown vertically with a velocity of 20 m s-1. The motion of the stone can be represented by a velocity-graph in Diagram 4.

Diagram 4

Find(a) the maximum height reached by the stone

Diagram 2

Diagram 1

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(b) the time taken for the stone to reach the maximum height(c) the deceleration experienced by the stone when it is being thrown upwards.

7. Diagram 5 shows a velocity-time graph of an object moving in a straight line. Find

(a) the acceleration of the object in the first 2 seconds(b) the distance travelled by the object when it is moving in constant velocity(c) the deceleration of the object in the time interval from t = 7 s to t = 11 s(d) the displacement at the final second(e) Sketch the corresponding acceleration - time graph for the object.

8. Diagram 6 shows the velocity-time graph of a particle moving in a straight line.

(a) What is the acceleration of the particle in the first 3 seconds of the motion?(b) What is the deceleration of the particle after 3 seconds?(c) What is the total distance travelled by the particle?(d) Find the displacement of the particle with respect to its original position after 8 seconds.(e) Sketch the corresponding acceleration-time graph of the particle.

9. Diagram 7 shows the velocity-time graph for a particle moving in 16 seconds.

Diagram 7

Find(a) the maximum acceleration of the particle(b) the deceleration of the particle(c) the total distance travelled by the particle(d) the average velocity of the particle

Diagram 6

Diagram 5

Page 8: Lesson 3

10. Diagram 8 shows the velocity-time graph of a particle moving in a straight line.

Diagram 8

(a) Name the sections of the graph which (i) acceleration of the particle(ii) deceleration of the particle

(b) Calculate(i) the total distance travelled by the particle(ii) the displacement of the particle of the last second

11. The graph in Diagram 9 shows the motion of a car from the time the driver of a car from the time the driver of a car from the time the driver of a car from the time the driver to see the traffic light.

Diagram 9

(a) The reaction time is the time interval in between the time when the traffic light is seen and the time at which the brake is applied. What is the reaction time?

(b) What is the distance travelled by the car before the brake is applied, starting from the time he spotted the traffic light?

(c) If the brake of the car is applied twice, calculate the greater deceleration experienced by the car.

(d) Determine the total distance travelled by the car before the car comes to a stop.(e) Sketch the corresponding acceleration-time graph for the whole journey of the car.

12. A car accelerates uniformly from rest and reaches a velocity of u m s-1 in 6 seconds. The car continues to move with this constant velocity for 28 seconds. Then, the brake is applied so that the

car decelerates uniformly for seconds before it stops.(a) Sketch a velocity-time graph of the motion of the car.(b) Given that the distance travelled when the brake is applied is two-third of the distance travelled

when the car is accelerating. Find the value of .

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(c) Given that the total distance travelled by the car is 495 m. Find the value of u.

13. The graph below shows the motion of an object.

What is the velocity of the object at t = 4 s?

A 0 m s-1 B 5 m s-1 C 10 m s-1 D 20 m s-1

14. The graph below shows the motion of an object

Which of the following statement is true?A The object at restB The object moves with uniform velocityC The object acceleratesD The object decelerates

15. The graph below shows for the motion of an object.

Which of the following statements is not true about the object?A The velocity of the object is increasingB The acceleration of the object is zeroC The displacement of the object is increasingD The gradient is constant

16. The graph below shows the motion of an object.

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Calculate the acceleration of the object

A 1.5 m s-2 B 2.5 m s-2 C 5.0 m s-2 D 7.5 m s-2

Past year question

1. SPM 2007 Paper 1 Question 5Diagram 1 is a velocity-time graph showing the motion of an object.

Diagram 1

Which of the following describes the motion of the object?

OJ JKA Uniform acceleration Decreasing accelerationB Increasing acceleration Decreasing accelerationC Increasing acceleration Uniform decelerationD Uniform acceleration Uniform deceleration

2. SPM 2008 Paper 1 Question 4Diagram 2 shows the velocity-time graph of an object.

Diagram 2

Which acceleration-time graph represents the same motion as the object?

A C

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B D

3. SPM 2009 Paper 1 Question 4

Diagram 3 shows a velocity-time graph for a motion of an object.

Diagram 3

What is the total distance, in m, travelled by the object in 8 s?

A. 18 B. 24 C.

32 D. 64

4. SPM 2010 Paper 1 Question 3Diagram 4 shows a car moving up a hill. The car decelerates as it moves up the hill and accelerates as it moves down the hill.

Diagram 4Which graph show the correct relationship between the velocity, v of the car and the time, t of the motion.

A C

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B D

5. SPM 2011 Paper 1 Question 10Diagram 8 shows a velocity-time graph for a motion of a toy car.

Diagram 8

What is the displacement of the car at 6 s?

A 0 m B 30 m C 45 m D 75 m

6. SPM 2012 Paper 1 Question 9Diagram 5 shows a velocity-time graph of a bus with passenger on board.After 10 minutes, the driver steps on the brake pedal to stop the bus.

Diagram 6

What is the velocity of the passengers immediately after the brake is applied?

A 0 m s-1 B 2 m s-1 C 6 m s-1 D 72 m s-1

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7. MRSM 2011 Paper 1 Question 4Diagram 7 shows a graph of velocity against time of a moving car.

Diagram 7

Which of the following explains the motion correctly?A Acceleration increases at a constant rate at PQB Deceleration is constant at RSC Velocity increases at a constant rate at RSD Velocity remains zero at QR

8. MRSM 2012 Paper 1 Question 4Which displacement-time graph represents the motion of a car with constant velocity?

A C

B D

9. MRSM 2013 Paper 1 Question 5Diagram 9 shows a displacement-time graph for the motion of a car.

Diagram 9

Based on the graph, which statement explains the motion of the car from A to B?

A Stationary B Decelerating C Accelerating D Constant velocity

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10. MRSM 2013 Paper 1 Question 6Diagram 10 shows a velocity-time graph for the motion of an object.

Diagram 10

What is the displacement of the object in the first 5 second?

A 20 m B 50 m C 70 m D 100 m

11. SBP 2007 Paper 1 Question 6Which of the following graphs shows an increasing acceleration?

A C

B D

12. SBP 2008 Paper 1 Question 3Which speed-time graph applies to an object at rest?

A C

B D

13. SBP 2008 Paper 1 Question 10

Page 15: Lesson 3

Diagram 13 shows the velocity-time graph for the motion of a car.

Diagram 13

Calculate the displacement travelled by the car.

A 80 m B 100 m C 120 m D 140 m

14. SBP 2010 Paper 1 Question 6Diagram 14 shows a graph of velocity against time for the motion of a bus.

Diagram 14

How far does the bus travel before it reaches a steady velocity?

A 10 m B 20 m C 100 m D 200 m

15. SBP 2014 Paper 1 Question 5Diagram 15 shows displacement-time graph of a moving object.

Diagram 15

Which velocity, v against time, t graph describe the motion of the object?

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A C

B D

16. MRSM 2014 Paper 1 Question 7Diagram 16 shows the velocity-time graph of a car.

Diagram 16

How far does the car travel before it reaches a constant velocity?

A 240 m B 400 m C 640 m D 3200 m