A particle has velocity v=4-2t m,s-1 for 0

Question

A particle has velocity v=4-2t m,s-1 for 0 <= t 4 seconds and initial displacement 1 m. Sketch its displacement–time, distance–time, velocity–time, speed–time and acceleration–time graphs, labelling endpoint values and any rest time. Distance means total distance since t=0.

Accepted Answer

$s=1+4t-t^2$ m; distance $D=4t-t^2$ before $2$ s and $D=t^2-4t+8$ afterwards. Velocity $4-2t$, speed $|4-2t|$ in $\mathrm{m\,s^{-1}}$; acceleration $-2\ \mathrm{m\,s^{-2}}$. Rest at $2$ s; endpoint distances $0,8$ m.

Five graphs of a reversing journey

Five graphs of a reversing journey

Solution:

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