Answer :
To determine the approximate stopping distance for a car traveling at 35 mph on a wet road, you can use the formula provided:
[tex]\[ a(v) = \frac{2.15 \times v^2}{64.4} \][/tex]
where:
- [tex]\( v \)[/tex] is the speed of the car in mph,
- [tex]\( 2.15 \)[/tex] is a constant factor related to the stopping condition (like road and car condition),
- [tex]\( 64.4 \)[/tex] is another constant that helps adjust the units or conditions for this formula.
### Step-by-step Solution:
1. Insert the given speed into the formula:
[tex]\[
v = 35 \, \text{mph}
\][/tex]
2. Substitute the values into the formula:
[tex]\[
a(35) = \frac{2.15 \times (35)^2}{64.4}
\][/tex]
3. Calculate [tex]\( 35^2 \)[/tex]:
[tex]\[
35^2 = 1225
\][/tex]
4. Multiply 2.15 by 1225:
[tex]\[
2.15 \times 1225 = 2637.5
\][/tex]
5. Divide by 64.4 to find the stopping distance:
[tex]\[
a(35) = \frac{2637.5}{64.4} \approx 40.9 \, \text{feet}
\][/tex]
Based on the calculation, the stopping distance for a car traveling at 35 mph on a wet road is approximately 40.9 feet. Therefore, the closest answer from the options given is 41.7 feet.
[tex]\[ a(v) = \frac{2.15 \times v^2}{64.4} \][/tex]
where:
- [tex]\( v \)[/tex] is the speed of the car in mph,
- [tex]\( 2.15 \)[/tex] is a constant factor related to the stopping condition (like road and car condition),
- [tex]\( 64.4 \)[/tex] is another constant that helps adjust the units or conditions for this formula.
### Step-by-step Solution:
1. Insert the given speed into the formula:
[tex]\[
v = 35 \, \text{mph}
\][/tex]
2. Substitute the values into the formula:
[tex]\[
a(35) = \frac{2.15 \times (35)^2}{64.4}
\][/tex]
3. Calculate [tex]\( 35^2 \)[/tex]:
[tex]\[
35^2 = 1225
\][/tex]
4. Multiply 2.15 by 1225:
[tex]\[
2.15 \times 1225 = 2637.5
\][/tex]
5. Divide by 64.4 to find the stopping distance:
[tex]\[
a(35) = \frac{2637.5}{64.4} \approx 40.9 \, \text{feet}
\][/tex]
Based on the calculation, the stopping distance for a car traveling at 35 mph on a wet road is approximately 40.9 feet. Therefore, the closest answer from the options given is 41.7 feet.
