High School

The table below shows the data for a car stopping on a wet road. What is the approximate stopping distance for a car traveling at 35 mph?

Car Stopping Distances

[tex]
\[
\begin{tabular}{|c|c|}
\hline
$v$ (mph) & $d$ (ft) \\
\hline
15 & 17.9 \\
20 & 31.8 \\
50 & 198.7 \\
\hline
\end{tabular}
\]
[/tex]

The stopping distance formula is given by:

[tex]
d(v) = \frac{2.15 v^2}{64.4 f}
[/tex]

Choose the approximate stopping distance from the options below:

A. 41.7 ft
B. 49.7 ft
C. 97.4 ft
D. 115.3 ft

Answer :

To find the approximate stopping distance for a car traveling at 35 mph on a wet road, you can use the following formula for stopping distance:

[tex]\[ d(v) = \frac{2.15 \times v^2}{64.4 \times f} \][/tex]

Where:
- [tex]\( v \)[/tex] is the speed in mph.
- [tex]\( f \)[/tex] is the friction factor. For wet roads, a typical value for [tex]\( f \)[/tex] is around 0.7.

Here are the steps to calculate the stopping distance:

1. Given Speed: The speed of the car is 35 mph.
2. Friction Factor: On wet roads, a typical friction factor [tex]\( f \)[/tex] is approximately 0.7.
3. Calculate the Stopping Distance:
- Insert the given values into the formula:
[tex]\[
d(35) = \frac{2.15 \times (35)^2}{64.4 \times 0.7}
\][/tex]
- Evaluate the expression:
[tex]\[
d(35) \approx 58.4 \text{ feet}
\][/tex]

Therefore, the approximate stopping distance for a car traveling at 35 mph on a wet road is about 58.4 feet.

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