Answer :
Sure! Let's determine the approximate stopping distance for a car traveling at 35 mph on a wet road using the provided formula:
1. Identify the values needed: To calculate the stopping distance, we need the speed of the car, which is 35 mph, and the coefficient of friction, which is typically estimated for a wet road. In this case, we assumed an estimated coefficient of friction of 0.7.
2. Use the formula: The stopping distance can be calculated using the formula:
[tex]\[
a(v) = \frac{2.15 \times v^2}{64.4 \times f}
\][/tex]
where [tex]\( v \)[/tex] is the speed in mph, and [tex]\( f \)[/tex] is the coefficient of friction.
3. Plug in the values:
[tex]\[
a(35) = \frac{2.15 \times 35^2}{64.4 \times 0.7}
\][/tex]
4. Calculate the intermediate values:
- First, calculate [tex]\( 35^2 \)[/tex], which is the square of the speed: [tex]\( 35^2 = 1225 \)[/tex].
- Next, multiply this by 2.15: [tex]\( 2.15 \times 1225 = 2638.75 \)[/tex].
5. Calculate the denominator:
- Multiply 64.4 by the coefficient of friction 0.7: [tex]\( 64.4 \times 0.7 = 45.08 \)[/tex].
6. Divide the results:
- Complete the division: [tex]\( \frac{2638.75}{45.08} \approx 58.42 \)[/tex].
So, the approximate stopping distance for a car traveling at 35 mph on a wet road is about 58.42 feet.
1. Identify the values needed: To calculate the stopping distance, we need the speed of the car, which is 35 mph, and the coefficient of friction, which is typically estimated for a wet road. In this case, we assumed an estimated coefficient of friction of 0.7.
2. Use the formula: The stopping distance can be calculated using the formula:
[tex]\[
a(v) = \frac{2.15 \times v^2}{64.4 \times f}
\][/tex]
where [tex]\( v \)[/tex] is the speed in mph, and [tex]\( f \)[/tex] is the coefficient of friction.
3. Plug in the values:
[tex]\[
a(35) = \frac{2.15 \times 35^2}{64.4 \times 0.7}
\][/tex]
4. Calculate the intermediate values:
- First, calculate [tex]\( 35^2 \)[/tex], which is the square of the speed: [tex]\( 35^2 = 1225 \)[/tex].
- Next, multiply this by 2.15: [tex]\( 2.15 \times 1225 = 2638.75 \)[/tex].
5. Calculate the denominator:
- Multiply 64.4 by the coefficient of friction 0.7: [tex]\( 64.4 \times 0.7 = 45.08 \)[/tex].
6. Divide the results:
- Complete the division: [tex]\( \frac{2638.75}{45.08} \approx 58.42 \)[/tex].
So, the approximate stopping distance for a car traveling at 35 mph on a wet road is about 58.42 feet.
