Velocity-Time Graphs (Edexcel International AS Maths): Revision Note
Exam code: XMA01
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Velocity-time graphs
What is a velocity-time graph?
Velocity- time graphs show the velocity of an object as it moves in a straight line
They show velocity (on the vertical axis) against time (on the horizontal axis)
Velocity-time graphs can go below the horizontal axis whereas speed-time graphs can not
What are the key features of a velocity-time graph?
The gradient of the graph equals the acceleration of an object
A straight line shows that the object is accelerating at a constant rate
A horizontal line shows that the object is moving at a constant velocity
The area between graph and the x-axis tells us the change in displacement of the object
Graph above the x-axis means the object is moving forwards
Graph below the x-axis means the object is moving backwards
The total displacement of the object from its starting point is the sum of the areas above the x-axis minus the sum of the areas below the x-axis
The total distance travelled by the object is the sum of all the areas
If the graph touches the x-axis then the object is stationary at that time
If the graph is above the x-axis then the object has positive velocity and is travelling forwards
If the graph is below the x-axis then the object has negative velocity and is travelling backwards
Worked Example
The motion of a bird travelling in a straight line is tracked for 60 seconds.
This information is displayed in the velocity-time graph below.
(a) Calculate the acceleration of the bird at 20 seconds.
Answer:
(b) Calculate the distance travelled in the first 28 seconds.
Answer:
(c) Calculate the displacement of the bird from its starting point after 60 seconds.
Answer:
Examiner Tips and Tricks
Be careful to spot if you are working with a distance-time graph or a velocity-time graph.
Be careful to spot if you are working with a speed-time graph or a velocity-time graph.
Check where the graph starts from on the y-axis, the velocity does not have to start at 0. For example, the scenario could be a car driving at a constant speed and the driver sees a hazard.
Be extra vigilant when working with negative gradients or with graphs under the x-axis, it is easy to make mistakes with these.
Speed is a scalar so it can not be negative whereas velocity can be.
Make sure your units are consistent.
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