11 A vehicle moves along a straight horizontal road. Points \(A\) and \(B\) lie on the road. As the vehicle passes point \(A\), it is moving with constant speed \(15 \mathrm {~ms} ^ { - 1 }\). It travels with this constant speed for 2 minutes before a constant deceleration is applied for 12 seconds so that it comes to rest at point \(B\).
a) Find the distance \(A B\). The vehicle then reverses with a constant acceleration of \(2 \mathrm {~ms} ^ { - 2 }\) for 8 seconds, followed by a constant deceleration of \(1.6 \mathrm {~ms} ^ { - 2 }\), coming to rest at the point \(C\), which is between \(A\) and \(B\).
b) Calculate the time it takes for the vehicle to reverse from \(B\) to \(C\).
c) Sketch a velocity-time graph for the motion of the vehicle.
d) Determine the distance \(A C\).