At time $$\(t\)$$ seconds $$\((0 \leqslant t< 5)\)$$, a particle $$\(P\)$$ has velocity $$\(\mathbf{v m ~ s}^{-1}\)$$, where $$\[ \mathbf{v}=(\sqrt{5-t}) \mathbf{i}+\left(t^{2}+2 t-3\right) \mathbf{j} \]$$ When $$\(t=\lambda\)$$, particle $$\(P\)$$ is moving in a direction parallel to the vector $$\(\mathbf{i}\)$$. (a) Find the acceleration of $$\(P\)$$ when $$\(t=\lambda\)$$ (5) The position vector of $$\(P\)$$ is measured relative to the fixed point $$\(O\)$$ When $$\(t=1\)$$, the position vector of $$\(P\)$$ is $$\((-2 \mathbf{i}+\mathbf{j}) \mathrm{m}\)$$. Given that $$\(1 \leqslant T< 5\)$$ (b) find, in terms of $$\(T\)$$, the position vector of $$\(P\)$$ when $$\(t=T\)$$ (5)

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