Displacement-time graphs - Higher

Displacement-time graphs show how the displacement of a moving object changes with time.

A horizontal line on a displacement-time graph shows that the object is stationary (not moving because the displacement does not change)

A sloping line on a displacement-time graph shows that the object is moving.

In a displacement-time graph, the slope or gradient of the line, is equal to the velocity of the object.

The steeper the line (and the greater the gradient) the faster the object is moving.

curriculum-key-fact
The gradient of a displacement–time graph = velocity

Example

Displacement graph
Section of graphWhat is represented
O - APositive constant velocity
velocity = gradient of displacement-time graph = displacement ÷ time
displacement = 4 m – 0 m = 4 m
time = 2 s – 0 s = 2 s
velocity = displacement ÷ time = 4 m ÷ 2 s = 2 m/s
A - BStopped
the displacement does not change: velocity = 0 m/s
B - CNegative constant velocity
the object is now travelling in the opposite direction
velocity = gradient of displacement-time graph = displacement ÷ time
displacement = 0 m – 4 m = -4 m
time = 8 s – 7 s = 1 s
velocity = displacement ÷ time = -4 m ÷ 1 s = -4 m/s
At Cthe object has returned to its starting position
the displacement is once again zero