When you double the velocity of an object, its kinetic energy increases by a factor of four. Here's why:

* Kinetic Energy Formula: The kinetic energy (KE) of an object is calculated using the following formula:

KE = (1/2) * m * v²

Where:

* m = mass of the object

* v = velocity of the object

* Doubling Velocity: If you double the velocity (v), the formula becomes:

KE = (1/2) * m * (2v)² = (1/2) * m * 4v² = 4 * (1/2) * m * v²

* Result: The new kinetic energy is four times the original kinetic energy.

In simpler terms: Kinetic energy is proportional to the square of the velocity. So, if you double the velocity, you square that increase, resulting in a fourfold increase in kinetic energy.