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M9.2MechanicsCore

Velocity-Time Graphs

A velocity-time graph carries two key pieces of information at once: the gradient is the acceleration, and the area under the line is the distance travelled. That makes it the most useful graph in kinematics.

25 min Video by Zeeshan Zamurred Constant Acceleration
Edexcel AS Level Maths: 9.2 Velocity-Time GraphsWatch the full walkthrough before the notes below.
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What you'll be able to do

  • Use gradient = acceleration
  • Use area under the graph = distance
  • Interpret a v–t graph
  • Calculate distance from a trapezium area
1

Gradient is acceleration

On a velocity-time graph, the is the . A horizontal line means constant velocity (zero acceleration); a negative gradient means deceleration.

Slope = acceleration.
2

Area is distance

The between the line and the time axis equals the travelled. For straight-line segments this is found by splitting the region into rectangles and triangles, or using the trapezium area.

Often a trapezium: .
1Area of triangle: .
Answer m

Tip — v–t graph: gradient = acceleration, AREA = distance. Don’t mix these up with the s–t graph.

3

Reading the motion

A rising line is acceleration, a falling line is deceleration, and a horizontal line is constant velocity. Where the line meets the time axis (), the object is momentarily at rest.

Formula recap

Acceleration from slope.
Distance from area.
Common area formula.

Common mistakes to avoid

Reading the gradient of a v–t graph as the velocity.
On a v–t graph the gradient is the ACCELERATION; velocity is the height.
Forgetting that the area gives distance.
Area under the v–t graph = distance travelled.

Key takeaways

  • v–t graph: gradient = acceleration, area = distance.
  • Horizontal line = constant velocity; falling line = deceleration.
  • Find distance via rectangle/triangle/trapezium areas.

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