"with urgent speed, with all possible haste," 1590s, from a noun (1530s) meaning "great speed," usually said to be from "post haste," an instruction formerly written on letters (attested from 1530s), from post (adv.) + haste (n.). The phrase originated in the old system of relaying messages by post horses (see post (n.3)); the verb post "to ride or travel with great speed" is recorded from 1550s.
musical instruction indicating a passage to be played with gradually increasing speed, 1842, from Italian accelerando, present participle of accelerare, from Latin accelerare "to hasten, quicken" (see accelerate).
c. 1200, rasen "to rush," from a Scandinavian source akin to the source of race (n.1), reinforced by the noun in English and by Old English cognate ræsan "to rush headlong, hasten, enter rashly." Transitive meaning "run swiftly" is from 1757. Meaning "run against in a competition of speed" is from 1809. Transitive sense of "cause to run" is from 1860. In reference to an engine, etc., "run with uncontrolled speed," from 1862; transitive sense is by 1932. Related: Raced; racing.