# Math Help - Car stopping distance

1. ## Car stopping distance

Well, I failed my driving permit test because of this one question...

If a car is going at 10mi per hour with a stopping distance of 20 feet. If the car was going 20 miles per hour how far would the stopping distance be?

Well here were the choices

20 - knew this was wrong
40 - chose this
6x - I was deciding this between 40 and 60
7x - I considered this way off.

How did I get this wrong?

2. double the speed ... the stopping distance is quadrupled.

3. When a car brakes all it's kinetic energy must be lost as heat. Since kinetic energy is proportional to the square of the speed/velocity doubling the speed will quadruple the stopping distance:

$E_{k1} = kv^2$

$E_{2k1} = k(2v)^2 = 4kv^2$

$\frac{E_{2k1}}{E_{k1}} = \frac{4kv^2}{kv^2} = 4$