We use a dielectric-response formalism to compute the induced charge density and the induced potential in a conductive two-dimensional (2D) material, traversed by a charged particle that moves on a perpendicular trajectory with constant velocity. By analyzing the electric force on the material via the Maxwell stress tensor, we showed that the polarization of the material can be decomposed into a conservative part related to the dynamic image force, and a dissipative part describing the energy and momentum transfer to the material, which is ultimately responsible for launching the plasma oscillation waves in the material. After showing that the launching dynamics is fully determined by the Loss function of the material, we used a conductivity model suitable for the terahertz to the midinfrared frequency range, which includes both the intraband and interband electron transitions in the material, to compute the real-space and time animations of the propagating plasma waves in the plane of the material. Finally, we used a stationary phase analysis to show that the plasmon wave crests go into an overdamped regime at large propagation distances, which are comparable to the distances where retardation effects are expected to emerge due to hybridization of the plasmon dispersion with the light line at long wavelengths.