Answer :
To find the approximate stopping distance for a car traveling at 35 mph on a wet road, we have a formula provided:
[tex]\[ a(v) = \frac{2.15 \times v^2}{64.4 \times f} \][/tex]
In this formula:
- [tex]\( v \)[/tex] represents the speed of the car in mph.
- [tex]\( f \)[/tex] is the friction coefficient, which on a typical wet road can be assumed to be around 0.7.
Let's break down the steps to find the stopping distance:
1. Identify the given values:
- The speed [tex]\( v \)[/tex] of the car is 35 mph.
- The friction coefficient [tex]\( f \)[/tex] is 0.7.
2. Substitute the given values into the formula:
- Replace [tex]\( v \)[/tex] with 35 mph.
- Replace [tex]\( f \)[/tex] with 0.7.
The formula becomes:
[tex]\[ a(35) = \frac{2.15 \times (35)^2}{64.4 \times 0.7} \][/tex]
3. Calculate [tex]\( 35^2 \)[/tex]:
- [tex]\( 35^2 = 1225 \)[/tex].
4. Plug in the value and simplify the equation:
[tex]\[ a(35) = \frac{2.15 \times 1225}{64.4 \times 0.7} \][/tex]
[tex]\[ a(35) = \frac{2637.75}{45.08} \][/tex]
5. Divide the values:
- [tex]\( a(35) \approx 58.42 \)[/tex].
Therefore, the approximate stopping distance for a car traveling 35 mph on a wet road is 58.42 feet.
[tex]\[ a(v) = \frac{2.15 \times v^2}{64.4 \times f} \][/tex]
In this formula:
- [tex]\( v \)[/tex] represents the speed of the car in mph.
- [tex]\( f \)[/tex] is the friction coefficient, which on a typical wet road can be assumed to be around 0.7.
Let's break down the steps to find the stopping distance:
1. Identify the given values:
- The speed [tex]\( v \)[/tex] of the car is 35 mph.
- The friction coefficient [tex]\( f \)[/tex] is 0.7.
2. Substitute the given values into the formula:
- Replace [tex]\( v \)[/tex] with 35 mph.
- Replace [tex]\( f \)[/tex] with 0.7.
The formula becomes:
[tex]\[ a(35) = \frac{2.15 \times (35)^2}{64.4 \times 0.7} \][/tex]
3. Calculate [tex]\( 35^2 \)[/tex]:
- [tex]\( 35^2 = 1225 \)[/tex].
4. Plug in the value and simplify the equation:
[tex]\[ a(35) = \frac{2.15 \times 1225}{64.4 \times 0.7} \][/tex]
[tex]\[ a(35) = \frac{2637.75}{45.08} \][/tex]
5. Divide the values:
- [tex]\( a(35) \approx 58.42 \)[/tex].
Therefore, the approximate stopping distance for a car traveling 35 mph on a wet road is 58.42 feet.
