- The points \(A\) and \(B\) lie on the same straight horizontal road.
Figure 2, on page 11, shows the speed-time graph of a cyclist \(P\), for his journey from \(A\) to \(B\).
At time \(t = 0 , P\) starts from rest at \(A\) and accelerates uniformly for 9 seconds until his speed is \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
He then travels at constant speed \(V \mathrm {~ms} ^ { - 1 }\)
When \(t = 42\), cyclist \(P\) passes \(B\).
Given that the distance \(A B\) is 120 m ,
- show that \(V = 3.2\)
- Find the acceleration of cyclist \(P\) between \(t = 0\) and \(t = 9\)
Cyclist \(P\) continues to cycle along the road in the same direction at the same constant speed, \(V \mathrm {~ms} ^ { - 1 }\)
When \(t = 6\), a second cyclist \(Q\) sets off from \(A\) and travels in the same direction as \(P\) along the same road. She accelerates for \(T\) seconds until her speed is \(3.6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
She then travels at constant speed \(3.6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
Cyclist \(Q\) catches up with \(P\) when \(t = 54\)
- On Figure 2, on page 11, sketch a speed-time graph showing the journeys of both cyclists, for the interval \(0 \leqslant t \leqslant 54\)
- Find the value of \(T\)
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2f2f89a6-cec4-444d-95d9-0112887d87eb-11_661_1509_292_278}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
A copy of Figure 2 is on page 13 if you need to redraw your answer to part (c).
Only use this copy of Figure 2 if you need to redraw your answer to part (c).
\includegraphics[max width=\textwidth, alt={}, center]{2f2f89a6-cec4-444d-95d9-0112887d87eb-13_666_1509_374_278}
\section*{Copy of Figure 2}