A particle, $$\(P\)$$, travels in a straight line, starting from a point $$\(O\)$$ with velocity $$\(6 \mathrm{~ms} \mathrm{~s}^{-1}\)$$. The acceleration of $$\(P\)$$ at time $$\(t \mathrm{~s}\)$$ after leaving $$\(O\)$$ is $$\(a \mathrm{~m} \mathrm{~s}^{-2}\)$$, where $$\[ \begin{array}{ll} a=-1.5 t^{\frac{1}{2}} & \text { for } 0 \leqslant t \leqslant 1, \\ a=1.5 t^{\frac{1}{2}}-3 t^{-\frac{1}{2}} & \text { for } t> 1 . \end{array} \]$$ Find the velocity of $$\(P\)$$ at $$\(t=1\)$$. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ .

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