7 A particle starts from rest at the point \(A\) and travels in a straight line until it reaches the point \(B\). The velocity of the particle \(t\) seconds after leaving \(A\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), where \(v = 0.009 t ^ { 2 } - 0.0001 t ^ { 3 }\). Given that the velocity of the particle when it reaches \(B\) is zero, find

1. the time taken for the particle to travel from \(A\) to \(B\),
2. the distance \(A B\),
3. the maximum velocity of the particle.