4 A small object of mass 0.4 kg is released from rest at a point 8 m above the ground. The object descends vertically and when its downwards displacement from its initial position is \(x \mathrm {~m}\) the object has velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). While the object is moving, a force of magnitude \(0.2 v ^ { 2 } \mathrm {~N}\) opposes the motion.

1. Show that \(v \frac { \mathrm {~d} v } { \mathrm {~d} x } = 10 - 0.5 v ^ { 2 }\).
2. Express \(v\) in terms of \(x\).
3. Find the increase in the value of \(v\) during the final 4 m of the descent of the object.