Final answer:
The distance required to stop a car varies directly as the square of its speed. If it takes 250 feet to stop a car traveling 60 mph, it would take approximately 937.5 feet to stop a car traveling 96 mph.
Step-by-step explanation:
To solve this problem, we need to use the concept of direct variation. The distance required to stop a car varies directly as the square of its speed. This means that if the speed of a car doubles, the distance required to stop the car will quadruple.
According to the problem, if it takes 250 feet to stop a car traveling 60 miles per hour, we can set up a proportion to find the distance required to stop a car traveling 96 miles per hour.
Let's set up the proportion:
(Distance at 60 miles per hour) / (Distance at 96 miles per hour) = (Speed at 96 miles per hour)^2 / (Speed at 60 miles per hour)^2
Plugging in the values:
(250 feet) / (x) = (96 mph)^2 / (60 mph)^2
Simplifying:
250 / x = (96^2) / (60^2)
Cross-multiplying:
250 * (60^2) = x * (96^2)
Solving for x:
x = (250 * (60^2)) / (96^2)
Calculating the value of x:
x = 937.5 feet
Therefore, it would take approximately 937.5 feet to stop a car traveling 96 miles per hour.