"convertible car with a soft top," 1954, from rag (n.1) + top (n.1).
Entries linking to ragtop
rag n.1
"torn or worn scrap of cloth," early 14c., probably from a Scandinavian source (compare Old Norse rögg "shaggy tuft, rough hair," earlier raggw-; Old Danish rag; see rug), or else a back-formation from ragged. It also may represent an unrecorded Old English cognate of Old Norse rögg. In any case, from Proto-Germanic *rawwa-, from PIE root *reue- (2) "to smash, knock down, tear up, uproot" (see rough (adj.)).
Also in Middle English "a hard, rough piece of stone" (late 13c.). As an insulting term for "newspaper, magazine" it dates from 1734; slang for "tampon, sanitary napkin" is attested from 1930s (on the rag "menstruating" is from 1948). Rags "tattered clothing" is from mid-14c.; in the jocular sense of "personal clothing" it is attested by 1855 (singular), American English. Rags-to-riches as a description of a tale of a rise from poverty to wealth is attested by 1896. Rag-picker is from 1860; rag-shop, one selling old clothes, is from 1829.
top n.1
"highest point," Old English top "summit, crest, tuft," from Proto-Germanic *toppa- (source also of Old Norse toppr "tuft of hair," Old Frisian top "tuft," Old Dutch topp, Dutch top, Old High German zopf "end, tip, tuft of hair," German Zopf "tuft of hair"); no certain connections outside Germanic except a few Romanic words probably borrowed from Germanic.
Few Indo-European languages have a word so generic, which can be used of the upper part or surface of just about anything. More typical is German, which has Spitze for sharp peaks (mountains), oberfläche for the upper surface of flat things (such as a table). The meaning "highest position" is from 1620s; the meaning "best part" is from 1660s. The sense of "dominant sexual partner" is by 1961.
To go over the top is World War I slang for "start an attack," in reference to the top of the trenches; as "beyond reasonable limits, too far" it is recorded from 1968. Top of the world as "position of greatest eminence" is from 1670s. Top-of-the-line (adj.) is by 1950.