Nucleocytoplasmic transport is mediated by the interaction of transport factors (TFs) with disordered phenylalanine-glycine (FG) repeats that fill the central channel of the nuclear pore complex (NPC). However, the mechanism by which TFs rapidly diffuse through multiple FG repeats without compromising NPC selectivity is not yet fully understood. In this study, we build on our recent NMR investigations showing that FG repeats are highly dynamic, flexible, and rapidly exchanging among TF interaction sites. We use unbiased long timescale all-atom simulations on the Anton supercomputer, combined with extensive enhanced sampling simulations and NMR experiments, to characterize the thermodynamic and kinetic properties of FG repeats and their interaction with a model transport factor. Both the simulations and experimental data indicate that FG repeats are highly dynamic random coils, lack intrachain interactions, and exhibit significant entropically driven resistance to spatial confinement. We show that the FG motifs reversibly slide in and out of multiple TF interaction sites, transitioning rapidly between a strongly interacting state and a weakly interacting state, rather than undergoing a much slower transition between strongly interacting and completely noninteracting (unbound) states. In the weakly interacting state, FG motifs can be more easily displaced by other competing FG motifs, providing a simple mechanism for rapid exchange of TF/FG motif contacts during transport. This slide-and-exchange mechanism highlights the direct role of the disorder within FG repeats in nucleocytoplasmic transport, and resolves the apparent conflict between the selectivity and speed of transport.