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. Acceleration–time: the area is the change in velocity, 2 x 4=8 m/s. A positive acceleration need not mean increasing speed: before t=2, velocity is negative.

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.

Acceleration–time: the area is the change in velocity, \(2\times4=8\text{ m/s}\). A positive acceleration need not mean increasing speed: before \(t=2\), velocity is negative.

Acceleration graphs

Acceleration graphs