\begin{enumerate}
  \item \hspace{0pt} [In this question $\mathbf { i }$ and $\mathbf { j }$ are perpendicular horizontal unit vectors.]
\end{enumerate}

A particle $P$ is moving with constant acceleration. At 2 pm , the velocity of $P$ is $( 3 \mathbf { i } + 5 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }$ and at 2.30 pm the velocity of $P$ is $( \mathbf { i } + 7 \mathbf { j } ) \mathrm { km } \mathrm { h } ^ { - 1 }$

At time $T$ hours after $2 \mathrm { pm } , P$ is moving in the direction of the vector $( - \mathbf { i } + 2 \mathbf { j } )$\\
(a) Find the value of $T$.

Another particle, $Q$, has velocity $\mathbf { v } _ { Q } \mathrm {~km} \mathrm {~h} ^ { - 1 }$ at time $t$ hours after 2 pm , where

$$\mathbf { v } _ { Q } = ( - 4 - 2 t ) \mathbf { i } + ( \mu + 3 t ) \mathbf { j }$$

and $\mu$ is a constant.

Given that there is an instant when the velocity of $P$ is equal to the velocity of $Q$,\\
(b) find the value of $\mu$.\\

\hfill \mbox{\textit{Edexcel M1 2021 Q5 [9]}}