1. A particle \(P\) moves such that at time \(t\) seconds its position vector, \(\mathbf { r }\) metres, relative to a fixed origin \(O\) is given by

$$\mathbf { r } = \left( \frac { 3 } { 2 } t ^ { 2 } - 3 t \right) \mathbf { i } + \left( \frac { 1 } { 3 } t ^ { 3 } - k t \right) \mathbf { j } ,$$ where \(k\) is a constant and \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular horizontal unit vectors.

1. Find an expression for the velocity of \(P\) at time \(t\).
2. Given that \(P\) comes to rest instantaneously, find the value of \(k\).