The theory of dislocation motion in materials with high Peierls stress relates dislocation mobility to the underlying kink mechanisms. While one has been able to describe certain qualitative features of dislocation behavior, important details of the atomic core mechanisms are lacking. We present a hybrid micro-meso approach to modeling the mobility of a single dislocation in Si in which the energetics of defect cores and kink mechanisms are treated by atomistic simulation, while dislocation motion under applied stress and at finite temperature is described through kinetic Monte Carlo. Three important aspects pertaining to treating the details of local structure and dynamics of kinks are incorporated in our approach: (1) Realistic complexity of (multiple) kink mechanisms in the dislocation core. (2) Full Peach-Koehler formalism for treatment of curved dislocation. (3) Detailed investigation of interaction between partials. This simulation methodology is used to calculate micron-scale dislocation mobility, with no adjustable parameters; specifically we obtain temperature and stress dependent velocity results that can be compared with experimental measurements.