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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 Constant Acceleration
Edexcel AS Level Maths: 9.1 Displacement-Time GraphsCurated by Kepler, not produced by us. Watch it 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
1

Gradient is velocity

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

velocity=change in displacementchange in time=gradient\text{velocity} = \dfrac{\text{change in displacement}}{\text{change in time}} = \text{gradient}
Velocity is the slope of the s–t graph.
2

Reading the motion

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

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

3

Calculating velocity

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

Example 1An object moves from 2 m to 14 m in 4 s (straight line). Find the velocity.
114−24=124\dfrac{14 - 2}{4} = \dfrac{12}{4}.
Answer33 m/s

Formula recap

v=ΔsΔt=gradientv = \dfrac{\Delta s}{\Delta t} = \text{gradient}
Velocity from an s–t graph.
horizontal line=at rest\text{horizontal line} = \text{at rest}
Zero gradient.
negative gradient=returning\text{negative gradient} = \text{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

Answer a few questions, then review anything you missed.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

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Related lessons

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