6 A puck, of mass \(m \mathrm {~kg}\), is moving in a straight line across smooth horizontal ice. At time \(t\) seconds, the puck has speed \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). As the puck moves, it experiences an air resistance force of magnitude \(0.3 m v ^ { \frac { 1 } { 3 } }\) newtons, until it comes to rest. No other horizontal forces act on the puck. When \(t = 0\), the speed of the puck is \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
Model the puck as a particle.

1. Show that $$v = ( 4 - 0.2 t ) ^ { \frac { 3 } { 2 } }$$
2. Find the value of \(t\) when the puck comes to rest.
3. Find the distance travelled by the puck as its speed decreases from \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) to zero.
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