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

Answer:

640 feet.

Step-by-step 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:

$\displaystyle 3600k=250\Rightarrow k=\frac{250}{3600}=\frac{25}{360}=\frac{5}{72}$

So, our equation is:

$\displaystyle d=\frac{5}{72}s^2$

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

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