A particle \(P\) of mass 5 kg moves along a horizontal straight line. At time \(t \mathrm{~s}\), the velocity of \(P\) is \(v \mathrm{~m} \mathrm{~s}^{-1}\) and its displacement from a fixed point \(O\) on the line is \(x \mathrm{~m}\). The forces acting on \(P\) are a force of magnitude \(\frac{500}{v} \mathrm{~N}\) in the direction \(O P\) and a resistive force of magnitude \(\frac{1}{2} v^{2} \mathrm{~N}\). When \(t=0, x=0\) and \(v=5\).
(a) Find an expression for \(v\) in terms of \(x\).
(b) State the value that the speed approaches for large values of \(x\).