- At time \(t\) seconds, where \(t \geqslant 0\), a particle \(P\) has velocity \(\mathbf { v } \mathrm { ms } ^ { - 1 }\) where
$$\mathbf { v } = \left( t ^ { 2 } - 3 t + 7 \right) \mathbf { i } + \left( 2 t ^ { 2 } - 3 \right) \mathbf { j }$$
Find
- the speed of \(P\) at time \(t = 0\)
- the value of \(t\) when \(P\) is moving parallel to \(( \mathbf { i } + \mathbf { j } )\)
- the acceleration of \(P\) at time \(t\) seconds
- the value of \(t\) when the direction of the acceleration of \(P\) is perpendicular to \(\mathbf { i }\)