# 3.02 Graphs of motion in one dimension

Graphs are a very useful way of representing an object's motion. In this section we will look at graphs of displacement, velocity and acceleration against time. After completing this section you should be able to:

• recall that the gradient of a displacement time graph represents velocity
• recall that the gradient of a velocity time graph represents acceleration
• recall that the area under a velocity time graph represents displacement
• use the facts listed above to sketch graphs to represent the motion of objects

## Displacement time graphs The diagram shows a displacement time graph for a car travelling with constant velocity. The displacement is measured from the start line and the graph starts as the car crosses this line. The displacement of the car from the start line is plotted vertically at regular time intervals.

The gradient of the graph is equal to the cars velocity i.e. v = Δs/Δt
As the car is travelling at a constant velocity the gradient of the graph is the same at all points i.e it has a constant gradient and therefore produces a straight line graph. The steepness of the gradient is determined by the velocity. A car travelling with a lower velocity would have a shallower gradient and a car travelling with a higher velocity would have a steeper gradient. If the cars velocity was changing the gradient of the graph would not be constant. If the velocity of the car was increasing the gradient of the graph would become steeper and if the cars velocity was decreasing the gradient would become shallower.