4 Particles \(P\) and \(Q\) move on a straight line \(A O B\). The particles leave \(O\) simultaneously, with \(P\) moving towards \(A\) and with \(Q\) moving towards \(B\). The initial speed of \(P\) is \(1.3 \mathrm {~ms} ^ { - 1 }\) and its acceleration in the direction \(O A\) is \(0.1 \mathrm {~m} \mathrm {~s} ^ { - 2 } . Q\) moves with acceleration in the direction \(O B\) of \(0.016 t \mathrm {~m} \mathrm {~s} ^ { - 2 }\), where \(t\) seconds is the time elapsed since the instant that \(P\) and \(Q\) started to move from \(O\). When \(t = 20\), particle \(P\) passes through \(A\) and particle \(Q\) passes through \(B\).

1. Given that the speed of \(Q\) at \(B\) is the same as the speed of \(P\) at \(A\), find the speed of \(Q\) at time \(t = 0\).
2. Find the distance \(A B\).