[In this question, $$\(\mathbf{i}\)$$ and $$\(\mathbf{j}\)$$ are horizontal unit vectors.] A particle $$\(A\)$$ of mass $$\(0.5 \mathrm{~kg}\)$$ is at rest on a smooth horizontal plane. At time $$\(t=0\)$$, two forces, $$\(\mathbf{F}_{1}=(-3 \mathbf{i}+2 \mathbf{j}) \mathrm{N}\)$$ and $$\(\mathbf{F}_{2}=(p \mathbf{i}+q \mathbf{j}) \mathrm{N}\)$$, where $$\(p\)$$ and $$\(q\)$$ are constants, are applied to $$\(A\)$$. Given that $$\(A\)$$ moves in the direction of the vector $$\((\mathbf{i}-2 \mathbf{j})\)$$, (a) show that $$\(2 p+q-4=0\)$$ (4) Given that $$\(p=5\)$$ (b) find the speed of $$\(A\)$$ at time $$\(t=4\)$$ seconds. (5)

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