\includegraphics{figure_2}

Two cars, $A$ and $B$, move on parallel straight horizontal tracks. Initially $A$ and $B$ are both at rest with $A$ at the point $P$ and $B$ at the point $Q$, as shown in Figure 2. At time $t = 0$ seconds, $A$ starts to move with constant acceleration $a$ m s$^{-2}$ for 3.5 s, reaching a speed of 14 m s$^{-1}$. Car $A$ then moves with constant speed 14 m s$^{-1}$.

\begin{enumerate}[label=(\alph*)]
\item Find the value of $a$.
[2]

Car $B$ also starts to move at time $t = 0$ seconds, in the same direction as car $A$. Car $B$ moves with constant acceleration of 3 m s$^{-2}$. At time $t = T$ seconds, $B$ overtakes $A$. At this instant $A$ is moving with constant speed.

\item On a diagram, sketch, on the same axes, a speed-time graph for the motion of $A$ for the interval $0 \leqslant t \leqslant T$ and a speed-time graph for the motion of $B$ for the interval $0 \leqslant t \leqslant T$.
[3]

\item Find the value of $T$.
[8]

\item Find the distance of car $B$ from the point $Q$ when $B$ overtakes $A$.
[1]

\item On a new diagram, sketch, on the same axes, an acceleration-time graph for the motion of $A$ for the interval $0 \leqslant t \leqslant T$ and an acceleration-time graph for the motion of $B$ for the interval $0 \leqslant t \leqslant T$.
[3]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M1 2016 Q6 [17]}}