7 A particle moves with a constant acceleration of \(( 0.1 \mathbf { i } - 0.2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 2 }\). It is initially at the origin where it has velocity \(( - \mathbf { i } + 3 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\). The unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are directed east and north respectively.

1. Find an expression for the position vector of the particle \(t\) seconds after it has left the origin.
2. Find the time that it takes for the particle to reach the point where it is due east of the origin.
3. Find the speed of the particle when it is travelling south-east.