At time $$\(t\)$$ seconds $$\((t \geqslant 0)\)$$, a particle $$\(P\)$$ has velocity $$\(\mathbf{v} \mathrm{m} \mathrm{s}^{-1}\)$$, where $$\[ \mathbf{v}=\left(3 t^{2}-4\right) \mathbf{i}+(2 t-4) \mathbf{j} \]$$ When $$\(t=0, P\)$$ is at the fixed point $$\(O\)$$. (a) Find the acceleration of $$\(P\)$$ at the instant when $$\(t=0\)$$ (2) (b) Find the exact speed of $$\(P\)$$ at the instant when $$\(P\)$$ is moving in the direction of the vector $$\((11 \mathbf{i}+\mathbf{j})\)$$ for the second time. (4) (c) Show that $$\(P\)$$ never returns to $$\(O\)$$. (4)

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