5 A particle \(P\) moves in a straight line. It starts from rest at \(A\) and comes to rest instantaneously at \(B\). The velocity of \(P\) at time \(t\) seconds after leaving \(A\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), where \(v = 6 t ^ { 2 } - k t ^ { 3 }\) and \(k\) is a constant.

1. Find an expression for the displacement of \(P\) from \(A\) in terms of \(t\) and \(k\).
2. Find an expression for \(t\) in terms of \(k\) when \(P\) is at \(B\). Given that the distance \(A B\) is 108 m , find
3. the value of \(k\),
4. the maximum value of \(v\) when the particle is moving from \(A\) towards \(B\).