A particle $$\(P\)$$ of mass $$\(0.5 \mathrm{~kg}\)$$ moves along the positive $$\(x\)$$-axis in the positive $$\(x\)$$ direction. At time $$\(t\)$$ seconds, $$\(t \geqslant 1, P\)$$ is $$\(x\)$$ metres from the origin $$\(O\)$$ and is moving with speed $$\(v \mathrm{~m} \mathrm{~s}^{-1}\)$$. The resultant force acting on $$\(P\)$$ has magnitude $$\(\frac{2}{x^{3}} \mathrm{~N}\)$$ and is directed towards $$\(O\)$$. When $$\(t=1, x=1\)$$ and $$\(v=3\)$$ Show that (a) $$\(v^{2}=\frac{4}{x^{2}}+5\)$$ (5) (b) $$\(t=\frac{a+\sqrt{b x^{2}+c}}{d}\)$$, where $$\(a, b, c\)$$ and $$\(d\)$$ are integers to be found. (7)

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