"hot rod or constructed car designed for maximum engine efficiency with no regard for style," 1954, from drag (n.) in the racing sense + -ster, perhaps abstracted from roadster.
Entries linking to dragster
drag n.
c. 1300, dragge, "dragnet," perhaps from a Scandinavian source (compare Old Norse dragga "a load," Swedish dragg "grapnel") or from Old English dræge "dragnet," related to dragan "to draw" (see drag (v.)).
From 1708 as "anything attached to a moving body that retards its progress." As the name of a device for retarding or stopping the rotation of wheels, 1795. Sense of "annoying, boring person or thing" is 1813, perhaps from the mechanical senses or the notion of something that must be dragged as an impediment.
Sense of "women's clothing worn by a man" is by 1870, perhaps originally theater slang, from the sensation of long skirts trailing on the floor (another guess is Yiddish trogn "to wear," from German tragen); drag queen "male transvestite or cross-dresser" is from 1941.
Drag racing (1947), is said to be from thieves' slang drag "automobile" (1935), perhaps ultimately from slang sense of "wagon, buggy" (1755), because a horse would drag it. By 1851 this was transferred to "street," as in the phrase main drag (which some propose as the source of the racing sense).
In addition to the time trials there are a number of "drag races" between two or more cars. They are run, not for record, but to satisfy the desire of most Americans to see who can get from here to there in the fastest time. [Popular Mechanics, January 1947]
-ster
Old English -istre, from Proto-Germanic *-istrijon, feminine agent suffix used as the equivalent of masculine -ere (see -er (1)). Also used in Middle English to form nouns of action (meaning "a person who ...") without regard for gender.
The genderless agent noun use apparently was a broader application of the original feminine suffix, beginning in the north of England, but linguists disagree over whether this indicates female domination of weaving and baking trades, as represented in surnames such as Webster, Baxter, Brewster, etc. (though modern spinster probably carries an originally female ending).
Also compare whitester "one who bleaches cloth;" kempster (c. 1400; Halliwell has it as kembster) "woman who cleans wool." Chaucer ("Merchant's Tale") has chidester "an angry woman" (the 17c. had scoldster). Also compare Middle English shepster (late 14c.) "dressmaker, female cutter-out," literally "shapester," sleestere (mid-15c.) "murderess, female killer" ("slay-ster"). Sewster "seamstress" (Middle English seuestre, late 13c. as a surname, also used of men) is still in Jonson but was obsolete or provincial after 17c. In Modern English, the suffix has been productive in forming derivative nouns (gamester,roadster,punster, rodster "angler," etc.).