Inspection vehicle shuttles between markers

An inspection vehicle moves along a straight service lane from depot \(A\). Its velocity \(t\) seconds after leaving \(A\) is \(v=3(t-2)(t-6)\text{ m s}^{-1}\), for \(0\leq t\leq8\). Marker \(B\) is \(32\) metres from \(A\) in the positive direction.

1. Find the displacement \(s\) of the vehicle from \(A\) at time \(t\).[2]
2. Show that the vehicle is at \(B\), then \(A\), then \(B\) at \(t=2\), \(t=6\) and \(t=8\), respectively.[3]
3. Find the total distance travelled during the \(8\) seconds.[3]