Answer :
To find the stopping distance of a car traveling at 35 mph, we can use the formula provided for calculating stopping distance:
[tex]\[ a(v) = \frac{2.15 \cdot v^2}{64.4} \][/tex]
where:
- [tex]\( v \)[/tex] is the velocity in miles per hour (mph),
- [tex]\( a(v) \)[/tex] is the stopping distance in feet.
Let's plug in the values and calculate the stopping distance step-by-step:
1. Identify the velocity: We are given that the car is traveling at [tex]\( v = 35 \)[/tex] mph.
2. Use the formula:
Substitute [tex]\( v = 35 \)[/tex] into the formula:
[tex]\[ a(35) = \frac{2.15 \cdot 35^2}{64.4} \][/tex]
3. Calculate [tex]\( 35^2 \)[/tex]:
[tex]\( 35^2 = 1225 \)[/tex].
4. Insert this into the formula:
[tex]\[ a(35) = \frac{2.15 \cdot 1225}{64.4} \][/tex]
5. Calculate the numerator:
[tex]\( 2.15 \times 1225 = 2637.5 \)[/tex].
6. Divide by 64.4 to get the stopping distance:
[tex]\[ a(35) = \frac{2637.5}{64.4} \][/tex]
7. Perform the division:
[tex]\[ a(35) \approx 40.90 \][/tex]
So, the stopping distance for a car traveling at 35 mph is approximately 40.9 feet.
[tex]\[ a(v) = \frac{2.15 \cdot v^2}{64.4} \][/tex]
where:
- [tex]\( v \)[/tex] is the velocity in miles per hour (mph),
- [tex]\( a(v) \)[/tex] is the stopping distance in feet.
Let's plug in the values and calculate the stopping distance step-by-step:
1. Identify the velocity: We are given that the car is traveling at [tex]\( v = 35 \)[/tex] mph.
2. Use the formula:
Substitute [tex]\( v = 35 \)[/tex] into the formula:
[tex]\[ a(35) = \frac{2.15 \cdot 35^2}{64.4} \][/tex]
3. Calculate [tex]\( 35^2 \)[/tex]:
[tex]\( 35^2 = 1225 \)[/tex].
4. Insert this into the formula:
[tex]\[ a(35) = \frac{2.15 \cdot 1225}{64.4} \][/tex]
5. Calculate the numerator:
[tex]\( 2.15 \times 1225 = 2637.5 \)[/tex].
6. Divide by 64.4 to get the stopping distance:
[tex]\[ a(35) = \frac{2637.5}{64.4} \][/tex]
7. Perform the division:
[tex]\[ a(35) \approx 40.90 \][/tex]
So, the stopping distance for a car traveling at 35 mph is approximately 40.9 feet.
