4 A particle P moves so that its position vector \(\mathbf { r }\) at time \(t\) is given by \(\mathbf { r } = ( 5 + 20 t ) \mathbf { i } + \left( 95 + 10 t - 5 t ^ { 2 } \right) \mathbf { j }\).
- Determine the initial velocity of P .
At time \(t = T , \mathrm { P }\) is moving in a direction perpendicular to its initial direction of motion.
- Determine the value of \(T\).
- Determine the distance of P from its initial position at time \(T\).