Question

The distance required to stop a car varies

directly as the square of its speed. If 250
feet are required to stop a car traveling 60
miles per hour, how many feet are required to
stop a car traveling 96 miles per hour?

Answer 1

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.