4 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 \(v = 5\).

1. Find an expression for \(v\) in terms of \(x\).
2. State the value that the speed approaches for large values of \(x\).