A particle moves in a straight line through the point $$\(O\)$$. The displacement of the particle from $$\(O\)$$ at time $$\(t \mathrm{~s}\)$$ is $$\(s \mathrm{~m}\)$$, where $$\[ \begin{array}{ll} s=t^{2}-3 t+2 & \text { for } 0 \leqslant t \leqslant 6, \\ s=\frac{24}{t}-\frac{t^{2}}{4}+25 & \text { for } t \geqslant 6 . \end{array} \]$$ At $$\(t=6\)$$, the particle hits a barrier at a point $$\(P\)$$ and rebounds. Find the velocity with which the particle arrives at $$\(P\)$$ and also the velocity with which the particle leaves $$\(P\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

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