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. Displacement–time: the gradient gives velocity; the particle travels to s=-4 before returning to the origin. Distance–time: accumulated distance never decreases. D=4t-t2 for 0 <= t 2, and D=t2-4t+8 for 2 <= t 4. Its gradient is speed.

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.

Displacement–time: the gradient gives velocity; the particle travels to \(s=-4\) before returning to the origin.

Distance–time: accumulated distance never decreases. \(D=4t-t^2\) for \(0\le t\le2\), and \(D=t^2-4t+8\) for \(2\le t\le4\). Its gradient is speed.

Displacement and distance graphs

Displacement and distance graphs