Old English sped "success, a successful course; prosperity, riches, wealth; luck; opportunity, advancement," from Proto-Germanic *spodiz (source also of Old Saxon spod "success," Dutch spoed "haste, speed," Old High German spuot "success," Old Saxon spodian "to cause to succeed," Middle Dutch spoeden, Old High German spuoten "to haste"), from PIE *spo-ti-, from root *spes- or *speh- "prosperity" (source also of Hittite išpai- "get full, be satiated;" Sanskrit sphira "fat," sphayate "increases;" Latin spes "hope," sperare "to hope;" Old Church Slavonic spechu "endeavor," spĕti "to succeed," Russian spet' "to ripen;" Lithuanian spėju, spėti "to have leisure;" Old English spōwan "to prosper").
Meaning "rapidity of movement, quickness, swiftness" emerged in late Old English (at first usually adverbially, in dative plural, as in spedum feran). Meaning "rate of motion or progress" (whether fast or slow) is from c. 1200. Meaning "gear of a machine" is attested from 1866. Meaning "methamphetamine, or a related drug," first attested 1967, from its effect on users.
Speed limit is from 1879 (originally of locomotives); speed-trap is from 1908. Speed bump is 1975; figurative sense is 1990s. Full speed is recorded from late 14c. Speed reading first attested 1965. Speedball "mix of cocaine and morphine or heroin" is recorded from 1909.
Old English spedan (intransitive) "to succeed, prosper, grow rich, advance," from the stem of speed (n.). Compare Old Saxon spodian, Middle Dutch spoeden "hasten," Old High German spuoton "to succeed, prosper," German sputen "make haste, hurry." Meaning "to go hastily from place to place, move rapidly" is attested from c. 1200. Transitive meaning "cause to advance toward success" is from mid-13c.; that of "send forth with quickness, give a high speed to" is first recorded 1560s; that of "to increase the work rate of" (usually with up) is from 1856. Meaning "drive an automobile too fast" is from 1908. Related: Speeded; sped; speeding.