6 A car, of mass \(m \mathrm {~kg}\), is moving along a straight horizontal road. At time \(t\) seconds, the car has speed \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). As the car moves, it experiences a resistance force of magnitude \(2 m v ^ { \frac { 5 } { 4 } }\) newtons. No other horizontal force acts on the car.

1. Show that $$\frac { \mathrm { d } v } { \mathrm {~d} t } = - 2 v ^ { \frac { 5 } { 4 } }$$ (1 mark)
2. The initial speed of the car is \(16 \mathrm {~ms} ^ { - 1 }\). Show that $$v = \left( \frac { 2 } { t + 1 } \right) ^ { 4 }$$ (5 marks)