Question

The stopping distance D of a car after the brakes have been applied varies directly as the square of the speed of R. If a car traveling 80 mph can stop in 400ft, How fast can a car travel and still stop in 144ft?

Answer 1

Direct variation equations have the following form:

`y=kx`

Where "k" is the Constant of variation.

In this case, analyzing the information given in the exercise, you know that the equation for that Direct variation has this form:

`D=kR^2`

You know that:

`D=400ft`

When:

`R=80mph`

So you need to make the conversion from feet to miles. Since:

`1mi=5280ft`

You get:

`(400ft)((1mi)/(5280ft))\approx0.076mi`

Then, you can find the value of "k" as following: