A particle \(P\) of mass \(m\,\text{kg}\) moves along a horizontal straight line against a resistive force of magnitude \(2mv^3\,\text{N}\), where \(v\,\text{m s}^{-1}\) is the velocity of \(P\) at time \(t\,\text{s}\). When \(t=0\), \(v=1\).

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

(b) Find the displacement of \(P\) from its initial position when \(t=6\).