1. A car moves in a straight line along a horizontal road. The car is modelled as a particle. At time \(t\) seconds, where \(t \geqslant 0\), the speed of the car is \(v \mathrm {~ms} ^ { - 1 }\)

At the instant when \(t = 0\), the car passes through the point \(A\) with speed \(2 \mathrm {~ms} ^ { - 1 }\)
The acceleration, \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\), of the car is modelled by $$a = \frac { 4 } { 2 + v }$$ in the direction of motion of the car.

1. Use algebraic integration to show that \(v = \sqrt { 8 t + 16 } - 2\) At the instant when the car passes through the point \(B\), the speed of the car is \(4 \mathrm {~ms} ^ { - 1 }\)
2. Use algebraic integration to find the distance \(A B\).