What does a horizontal line on a velocity–time graph show?

Constant velocity with zero acceleration.

How do you find the velocity at an instant from a curved displacement–time graph?

Draw a tangent at that point and find its gradient.

What does a negative gradient on a displacement–time graph show?

Velocity in the opposite direction to the positive direction.

How do you estimate the area under a curved graph?

Count squares, or divide into strips and use the trapezium rule.

Why is the average velocity of a return journey zero?

The total displacement is zero.

What does a decreasing but positive acceleration mean for the velocity?

The velocity is still increasing, but at a decreasing rate.

What happens to the velocity–time graph at terminal velocity?

It becomes horizontal because the acceleration is zero.

What are the units of the gradient of a velocity–time graph?

m s⁻² (metres per second squared).

Motion graphsEdexcel International A Level Physics: Flashcards

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What does the gradient of a displacement–time graph represent?

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What does the gradient of a displacement–time graph represent?: Velocity.
What does the gradient of a velocity–time graph represent?: Acceleration.
What does the area under a velocity–time graph represent?: Displacement.
What does the area under an acceleration–time graph represent?: Change in velocity.
What does a horizontal line on a displacement–time graph show?: The object is at rest.
What does a horizontal line on a velocity–time graph show?: Constant velocity with zero acceleration.
How do you find the velocity at an instant from a curved displacement–time graph?: Draw a tangent at that point and find its gradient.
What does a negative gradient on a displacement–time graph show?: Velocity in the opposite direction to the positive direction.
How do you estimate the area under a curved graph?: Count squares, or divide into strips and use the trapezium rule.
Why is the average velocity of a return journey zero?: The total displacement is zero.
What does a decreasing but positive acceleration mean for the velocity?: The velocity is still increasing, but at a decreasing rate.
What happens to the velocity–time graph at terminal velocity?: It becomes horizontal because the acceleration is zero.
What are the units of the gradient of a velocity–time graph?: m s⁻² (metres per second squared).

Exam questions on Motion graphs

A cyclist rides along a straight road. Her displacement–time graph is a straight line rising from 0 m to 60 m in the first 10 s, then horizontal for 5.0 s, then a straight line falling back to 0 m over the next 15 s.
Calculate the average velocity and the average speed of the cyclist for the whole 30 s.2 marks
A tram moves along a straight track. Its velocity increases uniformly from rest to 16 m s⁻¹ in 8.0 s, stays constant for 20 s, and then decreases uniformly to rest in 16 s.
Calculate the distance travelled by the tram while it is decelerating.2 marks
A steel ball is released from rest in a tall cylinder of oil. Its velocity increases from zero until the ball reaches a constant terminal velocity of 0.40 m s⁻¹. Its speed is measured at 0.20 s intervals from release and is 0, 0.15, 0.26, 0.33, 0.37 and 0.39 m s⁻¹ at times 0, 0.20, 0.40, 0.60, 0.80 and 1.0 s.
Describe how the acceleration of the ball changes during its fall and explain how this can be seen from its velocity–time graph.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).