- \hspace{0pt} [In this question, position vectors are given relative to a fixed origin.] At time \(t\) seconds, where \(t > 0\), a particle \(P\) has velocity \(\mathbf { v } \mathrm { m } \mathrm { s } ^ { - 1 }\) where
$$\mathbf { v } = 3 t ^ { 2 } \mathbf { i } - 6 t ^ { \frac { 1 } { 2 } } \mathbf { j }$$
- Find the speed of \(P\) at time \(t = 2\) seconds.
- Find an expression, in terms of \(t , \mathbf { i }\) and \(\mathbf { j }\), for the acceleration of \(P\) at time \(t\) seconds, where \(t > 0\)
At time \(t = 4\) seconds, the position vector of \(P\) is ( \(\mathbf { i } - 4 \mathbf { j }\) ) m.
- Find the position vector of \(P\) at time \(t = 1\) second.