2.1.4 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:
    • 

Worked Example

(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.

Exam Tip