- A research engineer is testing the effectiveness of the braking system of a car when it is driven in wet conditions.
The engineer measures and records the braking distance, \(d\) metres, when the brakes are applied from a speed of \(V \mathrm { kmh } ^ { - 1 }\).
Graphs of \(d\) against \(V\) and \(\log _ { 10 } d\) against \(\log _ { 10 } V\) were plotted.
The results are shown below together with a data point from each graph.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{fa4afaf4-fe5d-4f3a-b3de-9600d5502a49-24_631_659_699_285}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{fa4afaf4-fe5d-4f3a-b3de-9600d5502a49-24_684_684_644_1101}
\captionsetup{labelformat=empty}
\caption{Figure 6}
\end{figure}
- Explain how Figure 6 would lead the engineer to believe that the braking distance should be modelled by the formula
$$d = k V ^ { n } \quad \text { where } k \text { and } n \text { are constants }$$
with \(k \approx 0.017\)
Using the information given in Figure 5, with \(k = 0.017\)
- find a complete equation for the model giving the value of \(n\) to 3 significant figures.
Sean is driving this car at \(60 \mathrm { kmh } ^ { - 1 }\) in wet conditions when he notices a large puddle in the road 100 m ahead. It takes him 0.8 seconds to react before applying the brakes.
- Use your formula to find out if Sean will be able to stop before reaching the puddle.