In-chain donor/acceptor block copolymers comprised of alternating electron rich/poor moieties are emerging as promising semiconducting chromophores for use in organic photovoltaic devices. The mobilities of charge carriers in these materials are experimentally probed using gated organic field-effect transistors to quantify electron and hole mobilities, but a mechanistic understanding of the relevant charge diffusion pathways is lacking. To elucidate the mechanisms of electron and hole transport following excitation to optically accessible low-lying valence states, we utilize mean-field quantum electronic dynamics in the TDDFT formalism to explicitly track the evolution of these photo-accessible states. From the orbital pathway traversed in the dynamics, p- and n-type conductivities can be distinguished. The electronic dynamics of the studied polymers show the time-resolved transitions between the initial photoexcited state, a tightly-bound excitonic state that is dark to the ground state, and a partially charge separated state indicated by long-lived, out-of-phase charge oscillations along the polymer backbone. The frequency of these charge oscillations yields an insight into the characteristic mobilities of charge carriers in these materials. When the barycenters of the electron and hole densities are followed during the dynamics, a pseudo-classical picture for the translation of charge carrier densities along the polymer backbone emerges that clarifies a crucial aspect in the design of efficient organic photovoltaic materials.