8 A stone, of mass 0.05 kg , is moving along the smooth horizontal floor of a tank, which is filled with oil. At time \(t\), the stone has speed \(v\). As the stone moves, it experiences a resistance force of magnitude \(0.08 v ^ { 2 }\).
- Show that
$$\frac { \mathrm { d } v } { \mathrm {~d} t } = - 1.6 v ^ { 2 }$$
(2 marks)
- The initial speed of the stone is \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
Show that
$$v = \frac { 15 } { 5 + 24 t }$$
(5 marks)