6 A car accelerates from rest along a straight horizontal road. The car's engine produces a constant horizontal force of magnitude 4000 N .
At time \(t\) seconds, the speed of the car is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), and a resistance force of magnitude \(40 v\) newtons acts upon the car. The mass of the car is 1600 kg .

1. Show that \(\frac { \mathrm { d } v } { \mathrm {~d} t } = \frac { 100 - v } { 40 }\).
2. Find the velocity of the car at time \(t\).