Drawing Travel Graphs (Edexcel IAL Maths)

Spec point — 3.1

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

How do I draw an acceleration-time graph?

• Most of the time the acceleration will be constant so you have to draw horizontal lines

• There will be discontinuities in the graph if the object instantaneously changes from acceleration at a constant rate to moving with constant velocity

• The area between an acceleration-time graph and the x-axis is the change in velocity

• You might not be given the acceleration but instead expected to calculate it

  • Remember acceleration is the rate of change of velocity

  • If acceleration is constant then:

    • $\mathrm{Acceleration}=\frac{\mathrm{Change} \mathrm{in} \mathrm{velocity}}{\mathrm{Time}}$

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.

Answer:

(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.

Answer:

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

Answer:

Exam Hint

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