A particle \(P\) of mass 1 kg is moving along a straight line against a resistive force of magnitude \(\frac{10 \sqrt{v}}{(t+1)^{2}} \mathrm{~N}\), where \(v \mathrm{~m} \mathrm{~s}^{-1}\) is the speed of \(P\) at time \(t \mathrm{~s}\). When \(t=0, v=25\).

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