When a vehicle's speed is doubled, by how many times is the braking distance and destructive power in a crash increased?

When a vehicle's speed is doubled, the braking distance increases by four times due to the physics of motion. The relationship between speed and braking distance is governed by the laws of kinetic energy and the dynamics of stopping a vehicle.

Specifically, the kinetic energy of a vehicle is calculated using the formula: kinetic energy = 1/2 * mass * velocity^2. When the speed is increased, the kinetic energy increases with the square of the velocity. Therefore, if the speed is doubled (2 times the original speed), the new kinetic energy would be 1/2 * mass * (2 * velocity)^2, which simplifies to 1/2 * mass * 4 * (velocity)^2. This means that the kinetic energy is increased by a factor of four when the speed is doubled.

In terms of braking distance, the required distance to stop a vehicle is directly related to its initial kinetic energy, as more distance is needed to dissipate greater energy through braking. As such, when the speed is doubled, the braking distance also increases by a factor of four.

This principle also applies to the destructive power in a crash situation, as greater speed means not only more stopping distance but also greater impact forces during a collision,