9 Two particles \(A\) and \(B\) have position vectors \(\mathbf { r } _ { A }\) metres and \(\mathbf { r } _ { B }\) metres at time \(t\) seconds, where $$\mathbf { r } _ { A } = t ^ { 2 } \mathbf { i } + ( 3 t - 1 ) \mathbf { j } \quad \text { and } \quad \mathbf { r } _ { B } = \left( 1 - 2 t ^ { 2 } \right) \mathbf { i } + \left( 3 t - 2 t ^ { 2 } \right) \mathbf { j } , \quad \text { for } t \geqslant 0$$

1. Find the values of \(t\) when \(A\) and \(B\) are moving with the same speed.
2. Show that the distance, \(d\) metres, between \(A\) and \(B\) at time \(t\) satisfies $$d ^ { 2 } = 13 t ^ { 4 } - 10 t ^ { 2 } + 2$$
3. Hence find the shortest distance between \(A\) and \(B\) in the subsequent motion.