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

The only horizontal force acting on \(P\) has magnitude \(\dfrac1{10}(2v-1)^2e^{-t}\) N and acts towards \(O\). When \(t=0\), \(x=1\) and \(v=3\).

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

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