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

Answer:

SOLUTION: 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

Answer 2

Given:

The distance required to stop a car varies directly as the square of its speed. If 250 feet are required to stop a car travelling  60 miles per hour

To Find:

how many feet are required to stop a car  travelling 96 miles per hour?​

Solution:

It is given that the distance required to stop a car varies directly as the square of its speed, so we can formalize the equation as,

                                               $D\propto S^2$

where,

           D= distance required to stop the car

           S= Speed of the car

Now when we remove the proportionality sign a constant is added and the value of the constant can be found here by putting the values of the 1st situation, letting the constant be 'c'

$D=cS^2\\250=c*60*60\\c=\frac{5}{72}$

Now to find the value of the distance required when travelling 96 miles an hour, using the formulated equation to find the value,

$D=\frac{5}{72}*96*96\\=640ft$

Hence, 640feet are required to stop a car  travelling 96 miles per hour.