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The graph below shows a velocity - time graph for the motion of a particle. The motion has three stages.
Stage 1. The particle travels from rest with constant accleration for t=t1 seconds.
Stage 2. The particle travels at constant velocity from t = t1 to t=t2 seconds.
Stage 3. The particle travels with constant deceleration until it stops at time t=t3.
The area under the graph represents the total distance travelled.
Find the total distance travelled in these cases:
1 When constant acceleration = 1 ms-2, t1 = 3 seconds, t2 = 6 seconds, t3 = 9 seconds.
2 When constant acceleration = 1.5 ms-2, t1 = 4 seconds, t2 = 6 seconds, t3 = 12 seconds.

Summary/Background

Answers: 1. 18 m, 2. 42 m

Software/Applets used on this page

Cinderella
Uses Cinderella interactive geometry

Glossary

acceleration

the rate of change of velocity with time. It is a vector quantity with magnitude and direction.

constant

a value in a formula or equation that cannot change.

deceleration

negative acceleration, also known as retardation

graph

A diagram showing a relationship between two variables.
The diagram shows a vertical y axis and a horizontal x axis.

particle

an object with negligible size and internal structure, which can be represented by a point; the fundamental assumption in mechanics.

velocity

the rate of change of displacement. It is a vector quantity with magnitude and direction.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)M1KinematicsVelocity-time graphs-
AQA AS Maths 2017MechanicsKinematics and UnitsVelocity-Time Graphs-
AQA AS/A2 Maths 2017MechanicsKinematics and UnitsVelocity-Time Graphs-
CCEA A-Level (NI)M1KinematicsVelocity-time graphs-
CIE A-Level (UK)M1KinematicsVelocity-time graphs-
Edexcel A-Level (UK - Pre-2017)M1KinematicsVelocity-time graphs-
Edexcel AS Maths 2017MechanicsConstant Acceleration MotionVelocity-Time Graphs-
Edexcel AS/A2 Maths 2017MechanicsConstant Acceleration MotionVelocity-Time Graphs-
OCR A-Level (UK - Pre-2017)M1KinematicsVelocity-time graphs-
OCR AS Maths 2017MechanicsUnits and Motion BasicsVelocity-Time Graphs-
OCR MEI AS Maths 2017MechanicsWorking with MotionVelocity-Time Graphs-
OCR-MEI A-Level (UK - Pre-2017)M1KinematicsVelocity-time graphs-
Pre-U A-Level (UK)MechKinematicsVelocity-time graphs-
Universal (all site questions)KKinematicsVelocity-time graphs-
WJEC A-Level (Wales)M1KinematicsVelocity-time graphs-