Velocity-time graphs

Determining acceleration

If an object moves along a straight line, its motion can be represented by a velocity-time (or speed-time) graph. The gradient of the line is equal to the acceleration of the object.

A velocity/time graph. Graph with four distinct sections. All lines are straight.

The table shows what each section of the graph represents:

Section of graphGradientVelocityAcceleration
D (v = 0)ZeroStationary (at rest)Zero

Calculating displacement - Higher

The displacement of an object can be calculated from the area under a velocity-time graph.

The area under the graph can be calculated by:

  • using geometry (if the lines are straight)
  • counting the squares beneath the line (particularly if the lines are curved)


Calculate the total displacement of the object - its motion is represented by the velocity-time graph below.

The y axis shows velocity in metres per second and the x axis time in seconds.  The object increases its velocity from 0 metres per second to 8 metres per second in 4 seconds.

Here, the displacement can be found by calculating the total area of the shaded sections below the line.

1. Find the area of the triangle:

area of triangle = \frac{1}{2} × base × height

= \frac{1}{2} × 4 × 8 = 16 m2

2. Find the area of the rectangle:

area of rectangle = base × height

= (10 - 4) × 8 = 48 m2

3. Add the areas together to find the total displacement:

(16 + 48) = 64 m