Drawing Travel Graphs (AQA AS 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
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.
(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.
(c) Calculate the total time from the moment the brakes were first applied to the moment the train came to rest.
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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