A particle has acceleration 2 m,s-2 for 0

Question

A particle has acceleration 2 m,s-2 for 0<t<2 seconds and -1 m,s-2 for 2<t<6 seconds. Its velocity is continuous and initially -2 m,s-1. Sketch its velocity–time graph, labelling endpoint and rest values. Decide when it reverses direction.

Accepted Answer

$v=2t-2$ for $0\le t\le2$, then $v=4-t$ for $2\le t\le6$, in $\mathrm{m\,s^{-1}}$. End velocities are $-2,-2$; peak is $2$ at $2$ s. Reversals occur at $1,4$ s.

Recovering velocity from an acceleration graph

Recovering velocity from an acceleration graph

Solution:

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