Drawing Travel Graphs (Edexcel International A Level Maths: Mechanics 1)

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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-1-1-1

2.1.3 Drawing Travel Graphs Diagram 1 2, downloadable Edexcel A Level Mechanics revision notes

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:
      • begin mathsize 16px style Acceleration space equals fraction numerator Change space in space velocity over denominator Time end fraction end style

Worked example

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

osqtfJBQ_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 Tip

  • 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.

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Dan

Author: Dan

Expertise: Maths

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.