10 A student is attempting to model the flight of a boomerang.
She throws the boomerang from a fixed point \(O\) and catches it when it returns to \(O\).
She suggests the model for the displacement, \(s\) metres, after \(t\) seconds in given by
\(s = 9 t ^ { 2 } - \frac { 3 } { 2 } t ^ { 3 } , 0 \leq t \leq 6\). For this model,

1. determine what happens at \(t = 6\),
2. find the greatest displacement of the boomerang from \(O\),
3. find the velocity of the boomerang 1 second before the student catches it,
4. find the acceleration of the boomerang 1 second before the student catches it.