Nonlinear silicon photonics will play an important role in future integrated opto-electronic circuits. Here we report temporal pulse broadening induced by the dynamic interplay of nonlinear free-carrier dispersion coupled with group-velocity dispersion in nanostructured silicon waveguides for the first time, to the best of our knowledge. Further, we demonstrate that the nonlinear temporal dynamics are supported or countered by third-order dispersion, depending on the sign. Our time-domain measurements of the subpicojoule pulse dynamics are supported by strong agreement with numerical modeling. In addition to the fundamental nonlinear optical processes unveiled here, these results highlight dispersion engineering as a powerful tool for controlling free-carrier temporal effects.