A particle $$\(P\)$$ of mass 2 kg moving on a horizontal straight line has displacement $$\(x \mathrm{~m}\)$$ from a fixed point on the line and velocity $$\(v \mathrm{~m} \mathrm{~s}^{-1}\)$$ at time $$\(t \mathrm{~s}\)$$. The only horizontal force acting on $$\(P\)$$ is a variable force $$\(F \mathrm{~N}\)$$ which can be expressed as a function of $$\(t\)$$. It is given that $$\[ \frac{v}{x}=\frac{3-t}{1+t} \]$$ and when $$\(t=0, x=5\)$$. Find an expression for $$\(x\)$$ in terms of $$\(t\)$$. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ .

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