The increase of speed is a squared relationship. Three times the speed will have nine times the force of impact.

• A. True
• B. False
• C. It depends
• D. It is linear

Answer: (A)

When you stop a moving mass, the force you feel in the crash is tied to the energy that must be dissipated and how quickly that energy is removed. The energy to stop a mass is proportional to the square of its speed (kinetic energy = 1/2 m v^2). If you stop it over a fixed distance, the average stopping force is this energy divided by the distance, so F ∝ v^2. That means tripling the speed makes the required stopping force increase by 3^2 = 9. So the statement is true under the usual assumption that stopping distance (and mass) stay the same. If stopping distance changes due to safety features or other factors, the exact force can differ, but the general rule is that impact force grows with the square of speed.