3. A particle \(P\) moves in a horizontal plane such that, at time \(t\) seconds, its velocity is \(\mathbf { v } \mathrm { ms } ^ { - 1 }\), where \(\mathbf { v } = 2 t \mathbf { i } - t ^ { \frac { 1 } { 2 } } \mathbf { j }\). When \(t = 0 , P\) is at the point with position vector \(- 10 \mathbf { i } + \mathbf { j }\) relative to a fixed origin \(O\).

1. Find the position vector \(\mathbf { r }\) of \(P\) at time \(t\) seconds.
2. Find the distance \(O P\) when \(t = 4\).