Depends on what you mean by a particle. Only photons can travel at the speed of light because they have no mass. Any 'particle' than has mass, like electrons, neutrons, protons, etc. can only approach the speed of light, but they can never reach it. Particle accelerators can speed up electrons to something like 99.9999% the speed of light, but no matter how hard they try, it is impossible to reach 100% of the speed of light.
If you want to know why this is mathematically, I'd suggest you type into google, 'Gamma Function'.
Maybe someone who is good at LATEX can show you hear, just ask.