Answer :
Sure, let's find the approximate stopping distance for a car traveling at 35 mph on a wet road using the provided formula:
The formula given for the stopping distance [tex]\( d(v) \)[/tex] is:
[tex]\[ d(v) = \frac{2.15 \times v^2}{64.4 \times f} \][/tex]
Where:
- [tex]\( v \)[/tex] is the speed of the car in miles per hour (mph).
- [tex]\( f \)[/tex] is the coefficient of friction, which is provided as 0.7 for a wet road.
Let's break down the steps to calculate the stopping distance:
1. Identify the values:
- Speed ([tex]\( v \)[/tex]) = 35 mph
- Friction factor ([tex]\( f \)[/tex]) = 0.7
2. Plug in the values into the formula:
[tex]\[ d(35) = \frac{2.15 \times (35)^2}{64.4 \times 0.7} \][/tex]
3. Calculate [tex]\( (35)^2 \)[/tex]:
[tex]\[ (35)^2 = 1225 \][/tex]
4. Multiply by the constant 2.15:
[tex]\[ 2.15 \times 1225 = 2637.5 \][/tex]
5. Calculate the denominator:
[tex]\[ 64.4 \times 0.7 = 45.08 \][/tex]
6. Divide the result from step 4 by the result from step 5:
[tex]\[ \frac{2637.5}{45.08} \approx 58.42 \][/tex]
So, the approximate stopping distance for a car traveling at 35 mph on a wet road is about 58.42 feet.
The formula given for the stopping distance [tex]\( d(v) \)[/tex] is:
[tex]\[ d(v) = \frac{2.15 \times v^2}{64.4 \times f} \][/tex]
Where:
- [tex]\( v \)[/tex] is the speed of the car in miles per hour (mph).
- [tex]\( f \)[/tex] is the coefficient of friction, which is provided as 0.7 for a wet road.
Let's break down the steps to calculate the stopping distance:
1. Identify the values:
- Speed ([tex]\( v \)[/tex]) = 35 mph
- Friction factor ([tex]\( f \)[/tex]) = 0.7
2. Plug in the values into the formula:
[tex]\[ d(35) = \frac{2.15 \times (35)^2}{64.4 \times 0.7} \][/tex]
3. Calculate [tex]\( (35)^2 \)[/tex]:
[tex]\[ (35)^2 = 1225 \][/tex]
4. Multiply by the constant 2.15:
[tex]\[ 2.15 \times 1225 = 2637.5 \][/tex]
5. Calculate the denominator:
[tex]\[ 64.4 \times 0.7 = 45.08 \][/tex]
6. Divide the result from step 4 by the result from step 5:
[tex]\[ \frac{2637.5}{45.08} \approx 58.42 \][/tex]
So, the approximate stopping distance for a car traveling at 35 mph on a wet road is about 58.42 feet.
