[In this question $$\(\mathbf{i}\)$$ and $$\(\mathbf{j}\)$$ are perpendicular horizontal unit vectors.] A particle $$\(P\)$$ is moving with constant acceleration. At $$\(2 \mathrm{pm}\)$$, the velocity of $$\(P\)$$ is $$\((3 \mathbf{i}+5 \mathbf{j}) \mathrm{km} \mathrm{h}^{-1}\)$$ and at $$\(2.30 \mathrm{pm}\)$$ the velocity of $$\(P\)$$ is $$\((\mathbf{i}+7 \mathbf{j}) \mathrm{km} \mathrm{h}^{-1}\)$$ At time $$\(T\)$$ hours after $$\(2 \mathrm{pm}, P\)$$ is moving in the direction of the vector $$\((-\mathbf{i}+2 \mathbf{j})\)$$ (a) Find the value of $$\(T\)$$. (6) Another particle, $$\(Q\)$$, has velocity $$\(\mathbf{v}_{Q} \mathrm{~km} \mathrm{~h}^{-1}\)$$ at time $$\(t\)$$ hours after $$\(2 \mathrm{pm}\)$$, where $$\[ \mathbf{v}_{Q}=(-4-2 t) \mathbf{i}+(\mu+3 t) \mathbf{j} \]$$ and $$\(\mu\)$$ is a constant. Given that there is an instant when the velocity of $$\(P\)$$ is equal to the velocity of $$\(Q\)$$, (b) find the value of $$\(\mu\)$$. (3)

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