No, subatomic particles like electrons and quarks do not always move at the speed of light. In fact, according to our current understanding of physics, particles with mass cannot reach or exceed the speed of light.
Particles with mass, such as electrons and quarks, are subject to the principles of special relativity, which describe the behavior of objects moving at speeds close to the speed of light. Special relativity states that as an object with mass approaches the speed of light, its energy and momentum increase, and its mass appears to increase as well. However, it would require an infinite amount of energy to accelerate a particle with mass to the speed of light.
Particles with mass move at speeds much slower than the speed of light in most situations encountered in everyday life. For example, electrons in atoms typically move at speeds on the order of a few percent of the speed of light. Quarks, which are fundamental constituents of protons and neutrons, are also not observed to move at speeds approaching that of light.
It's worth noting that particles without mass, such as photons (particles of light), always travel at the speed of light in a vacuum. Since they have no rest mass, they are not subject to the same limitations as particles with mass.
In summary, subatomic particles with mass, like electrons and quarks, do not move at the speed of light. They have speeds significantly below the speed of light in most scenarios encountered in the universe.