During cooling, the kinetic energy of the molecules falls. Why does this happen?

During cooling, the kinetic energy of the molecules falls, be cause, when cooling a substace, the particles (molecules) slow down.

The kinetic energy is related to the speed, such that the lower speed the lower kinetic energy.

Particles can translate and vibrate, in the case of gases and liquids, and only vibrate (in the case of solids).

As a substance is cooled the particles get closer and the motion (translation and vibration), slows down. You can see by the equation of the kinetic energy (KE):

KE = [1/2]mass * (speed) ² that as the speed is lower the KE will also be lower.

Additionally, when the cooling does not drive a change of phase (gas to liquid, liquid to solid, or solid to gas), it drives a decrease on temperature. In this case you should know that the temperature is a measure of the kinetic energy: the lower the temperature, the lower the kinetic energy.

Kinetic energy is the energy if an energy in motion. Molecules in a substance has varying kinetic energies because they move at different speeds. During cooling heat is released to the environment. Thus, when heat is being released, the kinetic energy of the molecules decreases.