Calculating displacement using a velocity-time graph - Higher

curriculum-key-fact
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 of the graph are straight)
  • counting the squares beneath the line (particularly if the lines of the graph are curved)

Example

Calculate the total displacement of the object, whose 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.

The displacement can be found by calculating the total area of the shaded sections between the line and the time axis.

There is a triangle and a rectangle – the area of both must be calculated and added together to give the total displacement.

To find the area of the triangle:

area = \frac{\text{1}}{\text{2}} x base x height

area = \frac{\text{1}}{\text{2}} x 4 s x 8 m/s = 16m

To find the area of the rectangle:

area = base × height

area = (10 - 4) s × 8 m/s = 48 m

Add the areas together to find the total displacement:

Total displacement = (16 m + 48 m) = 64 m

Velocity-time graphSpeed-time graph
Gradient of graphAcceleration (m/s2)Rate of Change of Speed (m/s2)
Area under graphDisplacement (m)Distance (m)