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

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.

• 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.