"speed-increasing gear in an automobile," 1929, from over- + drive (n.). Earlier it was a transitive verb, "to drive too hard, work to exhaustion," Old English oferdrifan.
Entries linking to overdrive
over-
word-forming element meaning variously "above; highest; across; higher in power or authority; too much; above normal; outer; beyond in time, too long," from Old English ofer (from PIE root *uper "over"). Over and its Germanic relations were widely used as prefixes, and sometimes could be used with negative force. This is rare in Modern English, but compare Gothic ufarmunnon "to forget," ufar-swaran "to swear falsely;" Old English ofercræft "fraud."
In some of its uses, moreover, over is a movable element, which can be prefixed at will to almost any verb or adjective of suitable sense, as freely as an adjective can be placed before a substantive or an adverb before an adjective. [OED]
Among the old words not now existing are Old English oferlufu (Middle English oferlufe), literally "over-love," hence "excessive or immoderate love." Over- in Middle English also could carry a sense of "too little, below normal," as in over-lyght "of too little weight" (c. 1400), overlitel "too small" (mid-14c.), oversmall (mid-13c.), overshort, etc.
drive n.
1690s, "an act of driving, the action of driving," from drive (v.). Sense of "course upon which carriages are driven" is from 1816 (hence its use in road and street names). Meaning "an excursion by vehicle" is from 1785.
Golfing sense of "forcible blow" is from 1836; in cricket from 1827, later also in baseball. Meaning "organized effort to raise money" is by 1889, American English. Sense of "dynamism" is from 1908. As a motor engine transmission lever position, by 1963. The computing sense "location capable of storing and reading a disk, etc." is by 1963.