We present the first-principles determination of electronic stopping power for protons and α-particles in a semiconductor material of great technological interest: silicon carbide. The calculations are based on non-equilibrium simulations of the electronic response to swift ions using real-time time-dependent density functional theory (RT-TDDFT). We compare the results from this first-principles approach to those of the widely used linear response formalism and determine the ion velocity regime within which linear response treatments are appropriate. We also use the non-equilibrium electron densities in our simulations to quantitatively address the long-standing question of the velocity-dependent effective charge state of projectile ions in a material, due to its importance in linear response theory. We further examine the validity of the recently proposed centroid path approximation recently proposed for reducing the computational cost of acquiring stopping power curves from RT-TDDFT simulations.