In this study we have incorporated two time scales into the phase-field-crystal model of a binary alloy to explore different solute trapping properties as a function of crystal-melt interface velocity. With only diffusive dynamics, we demonstrate that the segregation coefficient, K as a function of velocity for a binary alloy is consistent with the model of Kaplan and Aziz where K approaches unity in the limit of infinite velocity. However, with the introduction of wavelike dynamics in both the density and concentration fields, the trapping follows the kinetics proposed by Sobolev [Phys. Lett. A 199, 383 (1995)], where complete trapping occurs at a finite velocity.