in contrast to the folksy dylan-esque single "now or never" song that the song was originally released as a b-side to, "move on fast" is described by yoko ono as an "offbeat pop/rock sound", which also draws from bop, big band swing, and "razor-sharp feminist rock." ben urich and ken bielen described the song as "a straight-ahead rocker that hits the ground running and never lets up." they also praise john lennon's guitar playing. john lennon biographer jon wiener claimed that the song has a "furious rock beat." he described ono's vocal as employing "a nervous, blank voice that qualifies as proto-new wave."