Old English sceort, scort, probably from Proto-Germanic *skurta- (cf. Old Norse skorta "to be short of," skort "shortness;" Old High German scurz "short"), from PIE root *sker- "to cut," with notion of "something cut off" (cf. Sanskrit krdhuh "shortened, maimed, small;" Latin curtus "short," cordus "late-born," originally "stunted in growth;" Old Church Slavonic kratuku, Russian korotkij "short;" Lithuanian skurstu "to be stunted," skardus "steep;" Old Irish cert "small," Middle Irish corr "stunted, dwarfish").
Meaning "rude" is attested from late 14c. To fall short is from archery. Short fuse in figurative sense of "quick temper" first attested 1968. Short story first recorded 1877. To make short work of is first attested 1570s. Phrase short and sweet is from 1530s.
Meaning "electrical short circuit" first recorded 1854 (the verbal phrase short circuit is recorded from 1867). Slang meaning "car" is attested from 1897; originally "street car," so called based on street cars (or the rides taken in them) being "shorter" than railroad cars.