7 The unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are directed east and north respectively. A yacht moves with a constant acceleration. At time \(t\) seconds the position vector of the yacht is \(\mathbf { r }\) metres. When \(t = 0\) the velocity of the yacht is \(( 2 \mathbf { i } - \mathbf { j } ) \mathrm { ms } ^ { - 1 }\), and when \(t = 10\) the velocity of the yacht is \(( - \mathbf { i } + \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).

1. Find the acceleration of the yacht.
2. When \(t = 0\) the yacht is 20 metres due east of the origin. Find an expression for \(\mathbf { r }\) in terms of \(t\).
3. 1. Show that when \(t = 20\) the yacht is due north of the origin.
   2. Find the speed of the yacht when \(t = 20\).