7 A particle travels in a straight line from \(A\) to \(B\) in 20 s . Its acceleration \(t\) seconds after leaving \(A\) is \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\), where \(a = \frac { 3 } { 160 } t ^ { 2 } - \frac { 1 } { 800 } t ^ { 3 }\). It is given that the particle comes to rest at \(B\).

1. Show that the initial speed of the particle is zero.
2. Find the maximum speed of the particle.
3. Find the distance \(A B\).