To find the stopping distance of a car traveling at 55 miles per hour, we will use the given formula:
[tex]\[ d = 0.05 v^2 + 2 v \][/tex]
Here, [tex]\( d \)[/tex] represents the stopping distance in feet, and [tex]\( v \)[/tex] is the speed of the car in miles per hour. Given that the speed of the car is 55 miles per hour, we will substitute [tex]\( v \)[/tex] with 55 in the formula.
1. Substitute [tex]\( v = 55 \)[/tex] into the formula:
[tex]\[ d = 0.05 (55)^2 + 2(55) \][/tex]
2. Calculate [tex]\( (55)^2 \)[/tex]:
[tex]\[ (55)^2 = 3025 \][/tex]
3. Multiply 0.05 by 3025:
[tex]\[ 0.05 \times 3025 = 151.25 \][/tex]
4. Multiply 2 by 55:
[tex]\[ 2 \times 55 = 110 \][/tex]
5. Add the results from steps 3 and 4 to find [tex]\( d \)[/tex]:
[tex]\[ 151.25 + 110 = 261.25 \][/tex]
Therefore, the approximate stopping distance of a car going 55 miles per hour is 261.25 feet.
From the given options:
- 110
- 260
- 150
- 300
The closest option to 261.25 is 260. Therefore, the correct answer is 260.
