(CIE 0606/2021/m/22/Q12)
A particle $P$ travels in a straight line so that, $t$ seconds after passing through a fixed point $O$, its velocity, $v \mathrm{~ms}^{-1}$, is given by
$v=\dfrac{t}{2 \mathrm{e}}$ for $0 \leqslant t \leqslant 2$,
$v=\mathrm{e}^{-\dfrac{t}{2}} \quad$ for $t>2$.
Given that, after leaving $O$, particle $P$ is never at rest, find the distance it travels between $t=1$ and $t=3 .$
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