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 in a vacuum.
The theory of relativity, specifically the theory of special relativity developed by Albert Einstein, states that the speed of light in a vacuum is an absolute constant and is the maximum speed at which information or energy can travel. This speed is approximately 299,792,458 meters per second.
Particles with mass, such as electrons and quarks, have what is called "rest mass." This means that when they are at rest, they have a certain amount of mass associated with them. According to special relativity, as an object with mass approaches the speed of light, its energy increases and its mass appears to increase as well. However, it requires an infinite amount of energy to accelerate a particle with mass to the speed of light, and therefore it is impossible for them to reach or exceed this speed.
Particles with mass can have different speeds depending on their energy. For example, in particle accelerators, electrons and quarks can be accelerated to high speeds but always remain below the speed of light. Their velocities are typically described as a fraction of the speed of light, such as a percentage or a decimal.