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Displacement-Time Graphs (AQA AS Maths): Revision Note

Dan Finlay

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AQA Maths: MechanicsEdexcel Maths: MechanicsOCR Maths A: Mechanics

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Displacement-Time Graphs

What is a displacement-time graph?

  • Displacement-time graphs show the displacement of an object from a fixed origin as it moves in a straight line

  • They show displacement (on the vertical axis) against time (on the horizontal axis)

  • Displacement-time graphs can go below the horizontal axis whereas distance-time graphs can not

    • Distance can not be negative whereas displacement can be

What are the key features of a displacement-time graph?

  • The gradient of the graph equals the velocity of the object

    • A positive gradient means the object is travelling forwards

    • A negative gradient means that the object is travelling backwards

    • The steeper the line, the greater the speed

  • A straight line shows that the object is moving at a constant velocity

  • A curved line shows that the object is accelerating or decelerating

  • A horizontal line shows that the object is stationary

  • If the graph touches the x-axis, then the object is at the origin at that time

2-1-1-displacement-time-graphs-diagram-1

How do I find the average speed and the average velocity of a journey?

Average space speed =  fraction numerator Total space distance space travelled over denominator Time space taken end fraction

  • The average speed can not be negative as speed is a scalar quantity and can only take a positive value

Average space velocity space equals space fraction numerator Displacement space from space starting space point over denominator Time space taken end fraction

  • The average velocity is a vector quantity and can be positive, zero or negative

Worked Example

An athlete is training by jogging in a straight line.

The displacement-time graph below shows the displacement of the athlete from her starting point throughout her motion.

Graph showing displacement versus time. Displacement: 0-11m. Time: 0-14s. Segments: 0-2s rising, 2-5s flat, 5-8s rising, 8-14s falling.

(a)   Calculate the velocity of the athlete during the first 2 seconds.

2-1-1-displacement-time-graphs-example-solution-1-a

(b)    Describe the motion of the athlete between the times of 2 seconds and 5 seconds.

2-1-1-displacement-time-graphs-example-solution-1-b

(c)   Calculate the velocity of the athlete at 10 seconds.

2-1-1-displacement-time-graphs-example-solution-c

(d)   Find the total distanced travelled by the athlete during the 14 seconds.

2-1-1-displacement-time-graphs-example-solution-d

Examiner Tips and Tricks

  • Be careful to spot if you are working with a displacement-time graph or a velocity-time graph.

  • Be careful to spot if you are working with a displacement-time graph or a distance-time graph

  • Check where the graph starts from on the y-axis, the object does not have to start at 0. For example, if the graph starts at 100, the scenario could be a student on a walk starting 100 m from their house.

  • Distance is a scalar so it can not be negative whereas displacement from a starting point can be.

  • Think about the units when calculating, make sure they are consistent.

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    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.