M9.1MechanicsCore

Displacement-Time Graphs

A displacement-time graph plots position against time. Its defining feature: the gradient is the velocity. Reading the slope tells you how fast — and in which direction — an object is moving.

20 min Video by Zeeshan Zamurred Constant Acceleration

Edexcel AS Level Maths: 9.1 Displacement-Time GraphsWatch the full walkthrough before the notes below.

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What you'll be able to do

Interpret a displacement-time graph
Use gradient = velocity
Read constant velocity and rest from the graph
Interpret negative gradients

Gradient is velocity

On a displacement-time graph the $gradient$ at any point equals the $velocity$ . A steeper line means faster motion.

velocity = \frac{change in displacement}{change in time} = gradient

Velocity is the slope of the s–t graph.

Reading the motion

A $straight line$ means constant velocity; a $horizontal line$ (zero gradient) means the object is at rest; a $negative gradient$ means it is moving back towards the start.

Tip — Horizontal line = stationary (not “stopped moving on the graph” — actually at rest).

Calculating velocity

For a straight segment, velocity is the change in displacement over the change in time between two points.

\frac{14 - 2}{4} = \frac{12}{4}

Answer

3

m/s

Formula recap

v = \frac{Δ s}{Δ t} = gradient

Velocity from an s–t graph.

horizontal line = at rest

Zero gradient.

negative gradient = returning

Moving back.

Common mistakes to avoid

Reading the area under an s–t graph as something meaningful.

On an s–t graph it is the GRADIENT (velocity) that matters, not area.

Thinking a horizontal line means constant speed.

A horizontal line means the object is at rest (velocity 0).

Key takeaways

On a displacement-time graph, gradient = velocity.
Straight line = constant velocity; horizontal = at rest.
Negative gradient = moving back towards the start.

Test yourself

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