In the last decade, sequencing methods like Hi-C have made it clear the genome is intricately folded, and that this organization contributes significantly to the control of gene expression and thence cell fate and behavior. Single-cell DNA tracing microscopy and polymer physics-based simulations of genome folding have proposed these population-scale patterns arise from motor-driven, heterogeneous movement, rather than stable 3D genomic architecture, implying that motion, rather than structure, is key to understanding genome function. However, tools to directly observe this motion in vivo have been limited in coverage and resolution. Here we describe TRansposon Assisted Chromatin Kinetic Imaging Technology (TRACK-IT), which combines a suite of imaging and labeling improvements to achieve ultra-resolution in space and time, with self-mapping transposons to distribute labels across the chromosome, uncovering dynamic behaviors across four orders of magnitude of genomic separation. We find that sequences separated by sub-megabase distances, typically 200-500 nm of nanometers apart, can transition to close proximity in tens of seconds - faster than previously hypothesized. This rapid motion is dependent upon cohesin and is exhibited only within certain genomic domains. Domain borders act as kinetic impediments to this search process, substantially slowing the rate and frequency of the transition to proximity. The genomic separation-dependent scaling of the search time for cis-interactions within a domain violates predictions of diffusion, suggesting motor driven folding. This distinctive scaling is lost following cohesin depletion, replaced with a behavior consistent with diffusion. Finally, we found cohesin containing cells exhibited rare, processive movements, not seen in cohesin depleted cells. These processive trajectories exhibit extrusion rates of ~2.7 kb/s across three distinct genomic intervals, faster than recent in vitro measurements and prior estimates from in vivo data. Taken together, these results reveal a genome in motion across multiple genomic and temporal scales, where motor-dependent extrusion divides the sequence, not into spatially separate domains, but into kinetically separated domains that experience accelerated local search.