So as I understand it: If you hit a wall at twice the speed you hit four times as hard? I often ask people this and everyone says "at twice the speed you hit twice as hard".
$K=\frac{1}{2}mv^2$ is very counter intuitive. I have read an explanation that seems to say gravity is acceleration and that's where the squared comes from.
Do we have anyway of knowing if the kinetic energy of an object outside of a gravity field is linear or quadratic? Could the gravity field somehow match the acceleration to give the $v^2$
Bonus question: If you get pulled over for speeding should you ever ask the policeman why kinetic energy is quadratic instead of linear? $K=\frac{1}{2}mv^2=$($300) dollar fine where I live.
