6 A student is modelling the motion of a small boat as it moves on a lake. When the speed of the boat is \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the engine is switched off. At time \(t\) seconds later, it has a velocity of \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and experiences a resistance force of magnitude \(20 v\) newtons. The mass of the boat is 80 kg . To set up a simple model for the motion of the boat, the student assumes that the water in the lake is still and that the boat travels in a straight line.

1. Explain how these two assumptions allow the student to create a simple model.
2. State one other assumption that the student should make.
3. 1. Express \(\frac { \mathrm { d } v } { \mathrm {~d} t }\) in terms of \(v\).
   2. Find an expression for \(v\) in terms of \(t\).