What does the area under a velocity–time graph represent?

Displacement (distance if all the area is counted as positive).

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

Constant velocity, so zero acceleration.

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

Motion in the negative direction (back towards the start).

Distance versus displacement?

Distance is the total path length; displacement is the change in position, with direction.

Average speed formula?

Total distance \div total time.

Why might you reject a root in a journey question?

It would give a negative time or speed.

Motion graphsEdexcel International A Level Maths: 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 (distance if all the area is counted as positive).
What does the area under an acceleration–time graph represent?: The 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, so zero acceleration.
What does a negative gradient on a displacement–time graph show?: Motion in the negative direction (back towards the start).
Distance versus displacement?: Distance is the total path length; displacement is the change in position, with direction.
Average speed formula?: Total distance $\div$ total time.
Area of a trapezium?: $\frac12(a+b)h$
What does the area under a speed–time graph give?: The distance travelled.
Why might you reject a root in a journey question?: It would give a negative time or speed.

Exam questions on Motion graphs

A sprinter's motion along a straight track is modelled by a velocity–time graph made of three straight-line sections. From t = 0 to t = 4 s, the velocity increases uniformly from 0 to 12 m s⁻¹. From t = 4 s to t = 10 s the velocity is constant at 12 m s⁻¹. From t = 10 s to t = 16 s the velocity decreases uniformly from 12 m s⁻¹ to 0.
Find the average speed of the sprinter over the 16 s.2 marks
A cyclist rides along a straight road. Her displacement–time graph from the start point consists of three straight-line sections: from t = 0 to t = 5 s the displacement increases uniformly from 0 to 20 m; from t = 5 s to t = 8 s the displacement stays at 20 m; from t = 8 s to t = 14 s the displacement decreases uniformly from 20 m to 0.
Find the total distance the cyclist has travelled by t = 14 s, and her displacement from the start at that time.2 marks
A lift starts from rest at the ground floor. Its acceleration–time graph consists of three horizontal sections: an acceleration of 1.5 m s⁻² from t = 0 to t = 4 s, no acceleration from t = 4 s to t = 10 s, and an acceleration of −2 m s⁻² from t = 10 s to t = 13 s.
Find the greatest speed of the lift, and show that the lift is at rest at t = 13 s.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).