The DMV manual says that
The faster you go, the less time you have to avoid a hazard or collision. The force of a 60 mph crash is not just twice as great as a 30 mph crash; it’s four times as great!
My physics is quite rusty, so I could not figure it out. I guess the above statement is correct, but how do we prove it?
I figured this out myself, but alternative methods or new ways of understanding are still welcome.