When a vehicle's speed is doubled, what happens to the energy of a collision?

When a vehicle's speed is doubled, the energy involved in a collision increases significantly due to the relationship between speed and kinetic energy. Kinetic energy is calculated using the formula KE = 1/2 mv^2, where m represents mass and v represents velocity.

If the speed is doubled, you would replace v with 2v in the kinetic energy formula. Thus, the kinetic energy becomes:

KE = 1/2 m(2v)^2 = 1/2 m(4v^2) = 4(1/2 mv^2).

This demonstrates that when the speed is doubled, the kinetic energy becomes four times greater, meaning the energy of the collision increases by a factor of four. This substantial increase in energy is critical to understanding the mechanics of collisions and their potential for causing damage or injury, as higher speeds result in significantly more force being exerted during a crash.