A particle has s=t2-4t m, for 0 <= t 4. Then v=2t-4 m/s and a=2 m/s2. It reverses at t=2. Each graph below describes the same journey. Velocity–time: the gradient is acceleration. Signed area is displacement change; here the negative and positive triangular areas cancel. Speed–time: reflect negative velocity above the time axis. Area is distance, 4+4=8 m. Speed decreases before the turn and increases afterwards.

A particle has \(s=t^2-4t\text{ m}\), for \(0\le t\le4\). Then \(v=2t-4\text{ m/s}\) and \(a=2\text{ m/s}^2\). It reverses at \(t=2\). Each graph below describes the same journey.

Velocity–time: the gradient is acceleration. Signed area is displacement change; here the negative and positive triangular areas cancel.

Speed–time: reflect negative velocity above the time axis. Area is distance, \(4+4=8\text{ m}\). Speed decreases before the turn and increases afterwards.

Velocity and speed graphs

Velocity and speed graphs