2. A car moves along a straight horizontal road with constant acceleration \(a \mathrm {~ms} ^ { - 2 }\)
where \(a > 0\) The car is modelled as a particle. At time \(t = 0\), the car passes point \(A\) and is moving with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) In the first three seconds after passing \(A\) the car travels 20 m . In the fourth second after passing \(A\) the car travels 10 m . The speed of the car as it passes point \(B\) is \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) Find the time taken for the car to travel from \(A\) to \(B\).
(8)