5 A golf ball, of mass \(m \mathrm {~kg}\), is moving in a straight line across smooth horizontal ground. At time \(t\) seconds, the golf ball has speed \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). As the golf ball moves, it experiences a resistance force of magnitude \(0.2 m v ^ { \frac { 1 } { 2 } }\) newtons until it comes to rest. No other horizontal force acts on the golf ball. Model the golf ball as a particle.

1. Show that $$\frac { \mathrm { d } v } { \mathrm {~d} t } = - 0.2 v ^ { \frac { 1 } { 2 } }$$
2. When \(t = 0\), the speed of the golf ball is \(16 \mathrm {~ms} ^ { - 1 }\). Show that \(v = ( 4 - 0.1 t ) ^ { 2 }\).
3. Find the value of \(t\) when \(v = 1\).
4. Find the distance travelled by the golf ball as its speed decreases from \(16 \mathrm {~ms} ^ { - 1 }\) to \(1 \mathrm {~ms} ^ { - 1 }\).