What happens to the average kinetic energy of the particles in a sample of matter as the temperature of the sample is increased?

Explanation:

The temperature of a substance is the measure of the average kinetic energy of its partilces.

The temperature, i.e. how hot or cold is a substance, is the result of the collisions of the particles (atoms or molecules) of matter.

The kinetic theory of gases states that, if the temperature is the same, the average kinetic energy of any gas is the same, regardless the gas and other conditions.

This equation expresses it:

Where Avg KE is the average kinetic energy, R is the universal constant of gases, N is Avogadro's constnat, and T is the temperature measure in absolute scale (Kelvin).

As you see, in that equation Avg KE is propotional to T, which means that as the temperature is increased, the average kinetic energy increases.