- At time \(t\) seconds, \(t > 0\), a particle \(P\) is at the point with position vector \(\mathbf { r } \mathrm { m }\), where
$$\mathbf { r } = \left( t ^ { 4 } - 8 t ^ { 2 } \right) \mathbf { i } + \left( 6 t ^ { 2 } - 2 t ^ { \frac { 3 } { 2 } } \right) \mathbf { j }$$
- Find the velocity of \(P\) when \(P\) is moving in a direction parallel to the vector \(\mathbf { j }\)
- Find the acceleration of \(P\) when \(t = 4\)