If you double your speed, how much longer will it take to stop?

When you double your speed, the stopping distance increases with the square of the speed. This principle is derived from the physics of motion, specifically the formula for kinetic energy and the relationship between stopping distance and speed.

The stopping distance of a vehicle is influenced by two main factors: the time it takes to perceive a hazard and the time it takes to apply the brakes. When you double your speed, the kinetic energy of the vehicle, which determines how much distance it covers during stopping, actually quadruples (because kinetic energy is proportional to the square of speed).

For example, if your original stopping distance at a certain speed is represented as D, when you double the speed to 2V, the new stopping distance becomes D × (2²), or 4D. Therefore, if you increase your speed, you must account for the fact that your vehicle will travel significantly farther before it can come to a complete stop.

This relationship illustrates why the correct answer is that it will take four times as much distance to stop if you double your speed.