# Velocity-time graphs

A useful form of graph that describes the way an object is moving is a velocity-time graph. The velocity of the object at any moment is plotted on the Y-axis and the time is plotted on the X-axis.

The graphs below show you how the velocity changes with time for a number of different examples.

The horizontal straight line shows something that is moving with a constant velocity.

Straight lines slanting upwards show objects whose velocity is increasing at a steady rate – they have constant positive acceleration. Straight lines slanting downwards show objects whose velocity is decreasing at a steady rate – they have a constant negative acceleration (retardation). The steeper the line the greater the acceleration or retardation.

A curved line shows an object whose acceleration is changing as time goes by.

We can use these graphs to work out the acceleration of an object.

Acceleration = change in velocity/time

and so the gradient of the line (change in velocity/time) gives us the acceleration

This is easy to do for a straight-line graph but for the curved line the acceleration is constantly changing and so we must measure the change in velocity over a small time interval to get an accurate answer.