Expedite
late 15th century (in the sense ‘perform quickly’): from Latin expedire ‘extricate (originally by freeing the feet), put in order’, from ex- ‘out’ + pes, ped- ‘foot’.
wiktionary
From Latin expedītus(“unimpeded, unfettered”), perfect passive participle of expediō(“bring forward, set right”).
etymonline
expedite (v.)
"to remove impediments to the movement or progress of, accelerate the motion or progress of, hasten, quicken," 1610s, from Latin expeditus, past participle of expedire "extricate, disengage, liberate; procure, make ready, put in order, make fit, prepare; explain, make clear," literally "free the feet from fetters," hence to liberate from difficulties, from ex "out" (see ex-) + *pedis "fetter, chain for the feet," related to pes (genitive pedis) "foot" (from PIE root *ped- "foot"). Compare Greek pede "fetter." Related: Expedited; expediting.