Velocity-Time Graph

What is Velocity-Time Graph?

A graph of a particle's velocity against time, from which two further quantities can be read directly. Its gradient at any instant is the acceleration at that instant, because acceleration is the rate of change of velocity with respect to time. The signed area between the graph and the time axis over an interval is the displacement over that interval, with area below the axis counting negatively because the particle is then moving in the negative direction. Distance travelled is obtained instead from the corresponding speed-time graph, in which the parts of the velocity graph below the axis are reflected above it, so that all area counts positively.

This definition is part of the Calculus chapter in Cambridge O Level Additional Mathematics.

Concepts related to Velocity-Time Graph

• gradient = acceleration
• signed area = displacement
• speed–time area = distance