5. A van of mass 1200 kg travels along a straight horizontal road against a resistance to motion which is proportional to the speed of the van. The engine of the van is working at a constant rate of 40 kW . The van starts from rest at time \(t = 0\). At time \(t\) seconds, the speed of the van is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). When the speed of the van is \(40 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the acceleration of the van is \(0.3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).

1. Show that $$75 v \frac { \mathrm {~d} v } { \mathrm {~d} t } = 2500 - v ^ { 2 }$$
2. Find \(v\) in terms of \(t\).