A particle \(P\) of mass \(m \mathrm{~kg}\) moves along a horizontal straight line with acceleration \(a \mathrm{~ms}^{-2}\) given by
\(a=\frac{v\left(1-2 t^{2}\right)}{t},\)
where \(v \mathrm{~m} \mathrm{~s}^{-1}\) is the velocity of \(P\) at time \(t \mathrm{~s}\).
(a) Find an expression for \(v\) in terms of \(t\) and an arbitrary constant.
(b) Given that \(a=5\) when \(t=1\), find an expression, in terms of \(m\) and \(t\), for the horizontal force acting on \(P\) at time \(t\).