2025 JVSS PRELIMS P2 Q9

A boat travelling in a straight line passes a buoy, \(B\), with a speed of \(v\) m/s. The velocity of the boat after passing \(B\) is given by \(v=t^2-5t+4\). The boat comes to rest momentarily, first at point \(C\) and then at point \(D\).

1. Find the distance \(CD\).[5]
2. Find the total distance travelled by the boat in the first 5 seconds after passing \(B\).[3]
3. Given that \(A\) is the point at which the boat has zero acceleration, determine with full working, whether \(A\) is nearer to \(B\) or to \(D\).[3]