A particle $$\(P\)$$ is moving in a plane with constant acceleration. The velocity, $$\(\mathrm{v} \mathrm{m} \mathrm{s}^{-1}\)$$, of $$\(P\)$$ at time $$\(t\)$$ seconds is given by $$\[ \mathbf{v}=(7-5 t) \mathbf{i}+(12 t-20) \mathbf{j} \]$$ (a) Find the speed of $$\(P\)$$ when $$\(t=2\)$$ (3) (b) Find, to the nearest degree, the size of the angle between the direction of motion of $$\(P\)$$ and the vector $$\(\mathbf{j}\)$$, when $$\(t=2\)$$ (3) The constant acceleration of $$\(P\)$$ is $$\(\mathbf{a m ~ s}{ }^{-2}\)$$ (c) Find $$\(\mathbf{a}\)$$ in terms of $$\(\mathbf{i}\)$$ and $$\(\mathbf{j}\)$$ (3) (d) Find the value of $$\(t\)$$ when $$\(P\)$$ is moving in the direction of the vector $$\((-5 \mathbf{i}+8 \mathbf{j})\)$$ (4)

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