for historical evolution, see V. Used punningly for you by 1588 ["Love's Labour's Lost," V.i.60], not long after the pronunciation shift that made the vowel a homonym of the pronoun. As a simple shorthand (without intentional word-play), it is recorded from 1862. Common in business abbreviations since 1923 (such as U-Haul, attested from 1951).
Entries linking to U
No native Anglo-Saxon words begin in v- except those (vane, vat, vixen) altered by the southwestern England habit of replacing initial f- with v- (and initial s- with z-). Confusion of -v- and -w- also was a characteristic of 16c. Cockney accents.
As a Roman numeral, "five." In German rocket weapons systems of World War II, it stood for Vergeltungswaffe "reprisal weapon." V-eight as a type of motor engine is recorded from 1929 (V-engine is attested from 1909), so called for the arrangement. The V for "victory" hand sign was conceived January 1941 by Belgian politician and resistance leader Victor de Laveleye, to signify French victoire and Flemish vrijheid ("freedom"). It was broadcast into Europe by Radio België/Radio Belgique and popularized by the BBC by June 1941, from which time it became a universal allied gesture.
Pronunciation of you and the nominative form ye gradually merged from 14c.; the distinction between them passed out of general usage by 1600. Widespread use of French in England after 12c. gave English you the same association as French vous, and it began to drive out singular nominative thou, originally as a sign of respect (similar to the "royal we") when addressing superiors, then equals and strangers, and ultimately (by c. 1575) becoming the general form of address. Through 13c. English also retained a dual pronoun ink "you two; your two selves; each other."