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 96miles per hour​

Answer 1

640 feet.

Explanation:

Let d represent the distance required to stop and let s represent the speed of the car.

The distance required to stop varies directly as the square of its speed. In other words:

`d=ks^2`

Where k is the constant of variation.

250 feet are required to stop a car traveling 60 miles per hour. Substitute:

`(250)=k(60)^2`

Simplify and solve for k:

`\displaystyle 3600k=250\Rightarrow k=(250)/(3600)=(25)/(360)=(5)/(72)`

So, our equation is:

`\displaystyle d=(5)/(72)s^2`

Then the distance required to stop a car traveling 96 miles per hour will be:

`\displaystyle d=(5)/(72)(96)^2=(5)/(72)(9216)=640\text{ feet}`