The energy of a moving object depends on its mass, but far more sharply on its speed. Because the speed is squared, going twice as fast carries four times the energy, which is exactly why a small rise in speed makes a crash so much worse.
Kinetic energy is the energy of a moving object: KE = ½mv², measured in joules. The velocity is squared, so doubling the speed multiplies the kinetic energy by four, not two.
Two identical cars race in, one at the speed you choose and one at double that speed, and both brake at the same line. Because kinetic energy depends on the square of the speed, the faster car carries four times the energy, so it needs four times the distance to stop. A small rise in speed makes the stop, and a crash, far worse.
The most common error is forgetting to square the velocity. KE = ½mv² means you square v first, then multiply by half the mass. Doubling the speed gives four times the kinetic energy, not twice. Writing ½mv (without the square) or doubling the energy when the speed doubles both lose marks.
A 0.50 kg ball moves at 8.0 m/s. Find its kinetic energy. Then find the kinetic energy if its speed doubles to 16 m/s.