Distance-time graphs show how the distance travelled by a moving object changes with time.

Part of

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)

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

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 = x base x height

area = 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 graph | Speed-time graph | |
---|---|---|

Gradient of graph | Acceleration (m/s^{2}) | Rate of Change of Speed (m/s^{2}) |

Area under graph | Displacement (m) | Distance (m) |