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.
trap n.
"contrivance for catching unawares," late Old English træppe, treppe "snare, trap," from Proto-Germanic *trep- (source also of Middle Dutch trappe "trap, snare"), related to Germanic words for "stair, step, tread" (Middle Dutch, Middle Low German trappe, treppe, German Treppe "step, stair," English tread (v.)).
This is probably literally "that on or into which one steps," from PIE *dreb-, an extended form of a root *der- (1), base of words meaning "to run, walk, step." The English word is probably akin to Old French trape, Spanish trampa "trap, pit, snare," but the exact relationship is uncertain.
The sense of "deceitful practice, device or contrivance to betray one" is recorded from c. 1400. The meaning "U-shaped section of a drain pipe" is from 1833. Slang meaning "mouth" is from 1776. Speed trap is by 1908. Trap-door "door in a floor or ceiling" (often hidden and leading to a passageway or secret place) is attested from late 14c. (trappe-dore).