5 A car is travelling at \(13 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) along a straight road when it passes a point \(A\) at time \(t = 0\), where \(t\) is in seconds. For \(0 \leqslant t \leqslant 6\), the car accelerates at \(0.8 t \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
- Calculate the speed of the car when \(t = 6\).
- Calculate the displacement of the car from \(A\) when \(t = 6\).
- Three \(( t , x )\) graphs are shown below, for \(0 \leqslant t \leqslant 6\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{470e70de-66ba-4dcc-a205-0c92f29471b1-3_382_458_1366_340}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{470e70de-66ba-4dcc-a205-0c92f29471b1-3_382_460_1366_881}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{470e70de-66ba-4dcc-a205-0c92f29471b1-3_384_461_1366_1420}
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{figure}
(a) State which of these three graphs is most appropriate to represent the motion of the car.
(b) For each of the two other graphs give a reason why it is not appropriate to represent the motion of the car.