A ball of mass \(2\,\text{kg}\) is projected vertically downwards with speed \(5\,\text{m s}^{-1}\) through a liquid. At time \(t\) seconds after projection, the velocity of the ball is \(v\,\text{m s}^{-1}\), and its displacement from its starting point is \(x\) metres.

The forces acting on the ball are its weight and a resistive force of magnitude \(0.2v^2\,\text{N}\).

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

(b) Deduce what happens to \(v\) for large values of \(t\).