A particle \(P\) is moving in a horizontal straight line. Initially \(P\) is at the point \(O\) on the line and is moving with velocity \(25 \mathrm{~m} \mathrm{~s}^{-1}\). At time \(t \mathrm{~s}\) after passing through \(O\), the acceleration of \(P\) is \(\frac{4000}{(5 t+4)^{3}} \mathrm{~ms}^{-2}\) in the direction \(P O\). The displacement of \(P\) from \(O\) at time \(t\) is \(x \mathrm{~m}\).

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