Velocity-time graphs - Higher

Velocity-time graphs show how the velocity of a moving object changes with time.

What is shown on the velocity-time graph?

A velocity/time graph. Graph with four distinct sections. All lines are straight.
  • Constant acceleration is shown by a straight rising line, A.
  • Constant retardation (or deceleration) is shown by a straight falling line, C.
  • Constant velocity is shown by a horizontal line, B.
  • A horizontal line along the X-axis shows the speed is zero, meaning that the vehicle has stopped, or is stationary, D.

The table shows what each section of the graph represents:

Section of graphGradientVelocityAcceleration
APositiveIncreasingPositive
BZeroConstantZero
CNegativeDecreasingNegative
DZeroStationary (at rest, v = 0)Zero

The slope or gradient of a velocity-time graph =

\frac{\text{final velocity – initial velocity}}{\text{time taken}} = acceleration

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The gradient of a velocity-time graph is the acceleration of the object.
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The steeper the line the greater the acceleration.

Example

Velocity-time graph above is for a racing car accelerating from rest.

The velocity-time graph above is for a racing car accelerating from rest.

Question

What is the acceleration in the first 10 s?

Acceleration = the gradient of the graph = \frac{\text{final velocity – initial velocity}}{\text{time taken}}

= (40 m/s – 0 m/s) ÷ 10 s

= 40 m/s ÷ 10 s

= 4 m/s2

The acceleration of the car in the first 10 s is 4 m/s2.

Question

What is the acceleration of the car between 30 s and 50 s?

Acceleration is the gradient of the graph = \frac{\text{final velocity – initial velocity}}{\text{time taken}}

= (0 m/s – 60 m/s) ÷ 20 s

= -60 m/s ÷ 20 s

= -3 m/s2

The car has an acceleration of -3 m/s2 (or a retardation of 3 m/s2).