Doubling your speed increases crash power by about how many times?

Doubling your speed increases crash power by about how many times?

• A. Two
• B. Three
• C. Four
• D. Eight

Answer: (C)

Doubling the speed changes how much energy must be dissipated in a crash, and that’s the key idea. The energy of a moving object is its kinetic energy, which is 1/2 m v^2. If you replace v with 2v, you get 1/2 m (2v)^2 = 4 × (1/2 m v^2). So the crash must deal with four times as much energy. If the stopping distance and how the vehicle brakes don’t change much, this extra energy shows up as about four times the peak force (and thus the crash power) because power is energy dissipated per unit time. Real crashes can vary due to crumple zones and deceleration time, but the general rule of thumb is that doubling speed makes the crash energy—and the resulting force/power—roughly four times greater. The other options would imply linear or different relationships that don’t match the v^2 scaling.

Doubling the speed changes how much energy must be dissipated in a crash, and that’s the key idea. The energy of a moving object is its kinetic energy, which is 1/2 m v^2. If you replace v with 2v, you get 1/2 m (2v)^2 = 4 × (1/2 m v^2). So the crash must deal with four times as much energy. If the stopping distance and how the vehicle brakes don’t change much, this extra energy shows up as about four times the peak force (and thus the crash power) because power is energy dissipated per unit time. Real crashes can vary due to crumple zones and deceleration time, but the general rule of thumb is that doubling speed makes the crash energy—and the resulting force/power—roughly four times greater. The other options would imply linear or different relationships that don’t match the v^2 scaling.