Answer :
To find the approximate stopping distance for a car traveling at 35 mph on a wet road, we use the formula provided:
[tex]\[ q(v) = \frac{2.15 \times v^2}{64.4 \times f} \][/tex]
where:
- [tex]\( v \)[/tex] is the speed of the car in miles per hour (mph),
- [tex]\( f \)[/tex] is the friction factor, which is typically assumed around 0.7 on wet roads.
Let's go through the steps to calculate this:
1. Identify the given speed: The car's speed, [tex]\( v \)[/tex], is 35 mph.
2. Use the typical friction factor for wet roads: Without a specific value given, we'll use [tex]\( f = 0.7 \)[/tex].
3. Plug these values into the formula:
[tex]\[ q(35) = \frac{2.15 \times (35)^2}{64.4 \times 0.7} \][/tex]
4. Perform the calculation:
- First, calculate [tex]\( 35^2 \)[/tex], which is 1225.
- Multiply 1225 by 2.15, getting 2637.75.
- Multiply 64.4 by 0.7, which is 45.08.
- Finally, divide 2637.75 by 45.08 to get approximately 58.42 ft.
The approximate stopping distance for a car traveling at 35 mph on a wet road is about 58.4 feet.
[tex]\[ q(v) = \frac{2.15 \times v^2}{64.4 \times f} \][/tex]
where:
- [tex]\( v \)[/tex] is the speed of the car in miles per hour (mph),
- [tex]\( f \)[/tex] is the friction factor, which is typically assumed around 0.7 on wet roads.
Let's go through the steps to calculate this:
1. Identify the given speed: The car's speed, [tex]\( v \)[/tex], is 35 mph.
2. Use the typical friction factor for wet roads: Without a specific value given, we'll use [tex]\( f = 0.7 \)[/tex].
3. Plug these values into the formula:
[tex]\[ q(35) = \frac{2.15 \times (35)^2}{64.4 \times 0.7} \][/tex]
4. Perform the calculation:
- First, calculate [tex]\( 35^2 \)[/tex], which is 1225.
- Multiply 1225 by 2.15, getting 2637.75.
- Multiply 64.4 by 0.7, which is 45.08.
- Finally, divide 2637.75 by 45.08 to get approximately 58.42 ft.
The approximate stopping distance for a car traveling at 35 mph on a wet road is about 58.4 feet.
