The relationship between speed and force of impact is quadratic.

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

Answer: (A)

When speed increases, the energy that must be dissipated during a crash grows with the square of speed. If you stop over a fixed distance, the average force required to stop is the work done to remove that energy divided by the stopping distance: F ≈ ΔK / d = (1/2 m v^2) / d. Since the stopping distance d is assumed constant, the force is proportional to v^2. In other words, doubling speed increases the stopping force by about a factor of four. This quadratic relationship shows why higher speeds produce disproportionately larger impact forces.

If stopping distance changed with speed, the relationship could differ, but with a constant stopping distance the force rises with the square of speed. That’s why the statement is true. The alternatives are inconsistent with this energy-over-distance reasoning: the force would not increase linearly, and it certainly wouldn’t decrease as speed rises.