Standard +0.3 This is a straightforward mechanics question requiring differentiation of position vectors to find velocity and acceleration, then applying simple conditions (parallel to j means i-component = 0) and calculating magnitude. All steps are routine M2 techniques with no novel problem-solving required, making it slightly easier than average.
3. At time \(t\) seconds \(( t \geqslant 0 )\) a particle \(P\) has position vector \(\mathbf { r }\) metres, with respect to a fixed origin \(O\), where
(b) the magnitude of the acceleration of \(P\) when \(t = 4\)
$$\begin{aligned}
& \qquad \mathbf { r } = \left( 16 t - 3 t ^ { 3 } \right) \mathbf { i } + \left( t ^ { 3 } - t ^ { 2 } + 2 \right) \mathbf { j } \\
& \text { Find } \\
& \text { (a) the velocity of } P \text { at the instant when it is moving parallel to the vector } \mathbf { j } \text {, }
\end{aligned}$$
VILIV SIHI NI IIIIIM ION OC
VILV SIHI NI JAHAM ION OC
VJ4V SIHI NI JIIYM ION OC
3. At time $t$ seconds $( t \geqslant 0 )$ a particle $P$ has position vector $\mathbf { r }$ metres, with respect to a fixed origin $O$, where\\
(b) the magnitude of the acceleration of $P$ when $t = 4$
$$\begin{aligned}
& \qquad \mathbf { r } = \left( 16 t - 3 t ^ { 3 } \right) \mathbf { i } + \left( t ^ { 3 } - t ^ { 2 } + 2 \right) \mathbf { j } \\
& \text { Find } \\
& \text { (a) the velocity of } P \text { at the instant when it is moving parallel to the vector } \mathbf { j } \text {, }
\end{aligned}$$
VILIV SIHI NI IIIIIM ION OC\\
VILV SIHI NI JAHAM ION OC\\
VJ4V SIHI NI JIIYM ION OC
\hfill \mbox{\textit{Edexcel M2 2018 Q3 [9]}}