1. A particle, \(P\), moves with constant acceleration \(( 2 \mathbf { i } - 3 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 2 }\)

At time \(t = 0\), the particle is at the point \(A\) and is moving with velocity ( \(- \mathbf { i } + 4 \mathbf { j }\) ) \(\mathrm { m } \mathrm { s } ^ { - 1 }\)
At time \(t = T\) seconds, \(P\) is moving in the direction of vector ( \(3 \mathbf { i } - 4 \mathbf { j }\) )

1. Find the value of \(T\). At time \(t = 4\) seconds, \(P\) is at the point \(B\).
2. Find the distance \(A B\).