The Particle-in-Cell (PIC) method for plasmons provides a mechanical, single-particle picture of plasmon resonances by tracking in time the movement of all the individual conduction electrons. By applying it to gold nanorods, we demonstrate the usefulness of PIC for extracting time-domain information of plasmons such as plasmon decay times, the relative contribution of each plasmon damping channel, detailed electron movement, as well as radiation and hot electron-emission during damping. An analysis of the time-resolved velocity distribution of the conduction electrons shows that only a small offset in this distribution in each cycle constitutes the plasmon oscillation. We show how PIC can be used to separately analyse Landau damping and Drude damping, and how their decay times can be calculated. Electron-electron scattering and surface scattering are both shown to gradually increase the overall kinetic energy of the electrons and decrease their coherence.