1. At time \(t = 0\), a toy electric car is at rest at a fixed point \(O\). The car then moves in a horizontal straight line so that at time \(t\) seconds \(( t > 0 )\) after leaving \(O\), the velocity of the car is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the acceleration of the car is modelled as \(( p + q v ) \mathrm { ms } ^ { - 2 }\), where \(p\) and \(q\) are constants.

When \(t = 0\), the acceleration of the car is \(3 \mathrm {~ms} ^ { - 2 }\)
When \(t = T\), the acceleration of the car is \(\frac { 1 } { 2 } \mathrm {~ms} ^ { - 2 }\) and \(v = 4\)

1. Show that $$8 \frac { \mathrm {~d} v } { \mathrm {~d} t } = ( 24 - 5 v )$$
2. Find the exact value of \(T\), simplifying your answer.