4 A particle of mass 0.5 kg moves along a horizontal straight line. Its velocity is \(v \mathrm {~ms} ^ { - 1 }\) at time \(t \mathrm {~s}\). The forces acting on the particle are a driving force of magnitude 50 N and a resistance of magnitude \(2 v ^ { 2 } \mathrm {~N}\). The initial velocity of the particle is \(3 \mathrm {~ms} ^ { - 1 }\).

1. Find an expression for \(v\) in terms of \(t\).
2. Deduce the limiting value of \(v\).