A particle \(P\) of mass \(2\,\text{kg}\) moves on a horizontal straight line. Its displacement from a fixed point \(O\) is \(x\) m and its velocity is \(v\,\text{m s}^{-1}\) at time \(t\) s.

The only horizontal force acting on \(P\) is a variable force \(F\) N which can be expressed as a function of \(t\). It is given that

and when \(t=0\), \(x=5\).

(a) Find an expression for \(x\) in terms of \(t\).

(b) Find the magnitude of \(F\) when \(t=3\).