7 A particle moves in a straight line through the point \(O\). The displacement of the particle from \(O\) at time \(t \mathrm {~s}\) is \(s \mathrm {~m}\), where
$$\begin{array} { l l }
s = t ^ { 2 } - 3 t + 2 & \text { for } 0 \leqslant t \leqslant 6 ,
s = \frac { 24 } { t } - \frac { t ^ { 2 } } { 4 } + 25 & \text { for } t \geqslant 6 .
\end{array}$$
- Find the value of \(t\) when the particle is instantaneously at rest during the first 6 seconds of its motion.
At \(t = 6\), the particle hits a barrier at a point \(P\) and rebounds. - Find the velocity with which the particle arrives at \(P\) and also the velocity with which the particle leaves \(P\).
- Find the total distance travelled by the particle in the first 10 seconds of its motion.
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