2025 DSS PRELIMS P1 Q9

A cyclist starts from rest from a point \(A\) and travels in a straight line until she comes to a rest at a point \(B\). During the motion, her velocity, \(v\) m/s, is given by \(v = 12t - \frac{3}{2}t^2\), where \(t\) is the time in seconds after leaving \(A\).

1. Find the time taken for the cyclist to travel from \(A\) to \(B\).[1]
2. Find the distance \(AB\).[3]
3. Find the acceleration of the cyclist when \(t = 5\).[2]