0

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?

Edit

I figured this out myself, but alternative methods or new ways of understanding are still welcome.

Jim
  • 24,676
Use your head
  • 159

1 Answers1

6

This is pretty basic physics:
We know the following formulae

$$F=ma$$ $$a={v_f^2-v_i^2\over2\Delta d}$$ In both cases, the final velocity is $0$. Assuming you have the same room, $\Delta d$, to decelerate in a crash,

$$F=m{v^2\over2\Delta d}$$

Due to the square of the velocity, if you increase the impact speed by a factor of 2, you increase the impact force by a factor of 4.

Jim
  • 24,676