Drawing Travel Graphs (Edexcel A Level Maths) : Revision Note

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Drawing Travel Graphs

How do I draw a displacement-time graph or a velocity-time graph?

  • You may be asked to draw a displacement-time graph or a velocity-time graph

  • You will be given information about different sections of a journey and must draw each section and label the points on the axes

  • Remember that time will always be on the x-axis

  • Always remember to include units when you label the axis

  • Use appropriate facts about the gradient and area under the graph to work backwards and find relevant or missing information

    • The gradient of a displacement-time graph is the velocity and the gradient of a velocity-time graph is the acceleration

    • The area between a velocity-time graph and the x-axis is the displacement

2-1-3-drawing-travel-graphs-diagram-1-1
2-1-3-drawing-travel-graphs-diagram-1-2

Worked Example

The driver of a train, travelling at 40 m s-1 on a straight horizontal track, is informed of debris on the track 0.74 km ahead and immediately applies the brakes.
The train decelerates uniformly for 20 seconds to a speed of 12 m s-1
The train then maintains this speed for another 8 seconds.
The driver reapplies the brakes to slow down the train at a constant rate and bring it to a complete stop 10 m before the debris.

(a)  Sketch a velocity-time graph to show the motion of the train.

hJKsbARD_2-1-3-drawing-travel-graphs-example-solution-a

(b) Find the deceleration of the train from the moment the brakes were first applied to the moment its speed first reached 12 m s-1.

2-1-3-drawing-travel-graphs-example-solution-b

(c) Calculate the total time from the moment the brakes were first applied to the moment the train came to rest.

2-1-3-drawing-travel-graphs-example-solution-c

Examiner Tips and Tricks

  • As in the worked example, examiners can use other words, such as uniformly, to mean constant.

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

  • Remember that displacement and velocity can be negative whereas distance and speed can not be negative.

  • Take care when a velocity-time graph is below the x-axis, if it has a negative gradient then it is speeding up and moving backwards. If it has a positive gradient below the x-axis then it is still moving backwards but it is slowing down.

  • Think about the units when calculating displacement, velocity and acceleration.

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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.

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