1. Two particles $A$ and $B$, of masses 2 kg and 5 kg respectively, are moving in the same direction along a smooth horizontal surface when they collide directly. Before the collision, $B$ is moving with speed $1.2 \mathrm {~ms} ^ { - 1 }$ and, immediately after the collision, its speed is $3.8 \mathrm {~ms} ^ { - 1 }$. The coefficient of restitution between the particles $A$ and $B$ is 0.3 .
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Find the impulse exerted by $A$ on $B$.
\item Given that the particles $A$ and $B$ were in contact for 0.08 seconds, find the average force between $A$ and $B$. \\[0pt]
[4]
\end{enumerate}\item Calculate the speed of $A$ before and after the collision.
\item After the collision between $A$ and $B$, particle $B$ continues to move with speed $3.8 \mathrm {~ms} ^ { - 1 }$ until it collides directly with a stationary particle $C$ of mass 4 kg . When $B$ and $C$ collide, they coalesce to form a single particle.
\begin{enumerate}[label=(\roman*)]
\item Write down the coefficient of restitution between $B$ and $C$.
\item Determine the speed of the combined particle after the collision.\\

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\end{enumerate}\end{enumerate}

\hfill \mbox{\textit{WJEC Further Unit 3 2024 Q1 [14]}}