3\\
\includegraphics[max width=\textwidth, alt={}, center]{c9e725ad-561b-4e98-9b8f-7c9d3c8e67e6-2_153_1009_978_570}

Three particles $P , Q$ and $R$, are travelling in the same direction in the same straight line on a smooth horizontal surface. $P$ has mass $m \mathrm {~kg}$ and speed $9 \mathrm {~m} \mathrm {~s} ^ { - 1 } , Q$ has mass 0.8 kg and speed $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $R$ has mass 0.4 kg and speed $2.75 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ (see diagram).\\
(i) A collision occurs between $P$ and $Q$, after which $P$ and $Q$ move in opposite directions, each with speed $3.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. Calculate
\begin{enumerate}[label=(\alph*)]
\item the value of $m$,
\item the change in the momentum of $P$.\\
(ii) When $Q$ collides with $R$ the two particles coalesce. Find their subsequent common speed.
\end{enumerate}

\hfill \mbox{\textit{OCR M1 2010 Q3 [9]}}