dust (n.) Look up dust at Dictionary.com
Old English dust, from Proto-Germanic *dunstaz (cognates: Old High German tunst "storm, breath," German Dunst "mist, vapor," Danish dyst "milldust," Dutch duist), from PIE *dheu- (1) "dust, smoke, vapor" (cognates: Sanskrit dhu- "shake," Latin fumus "smoke"). Meaning "that to which living matter decays" was in Old English, hence, figuratively, "mortal life."
dust (v.) Look up dust at Dictionary.com
c.1200, "to rise as dust;" later "to sprinkle with dust" (1590s) and "to rid of dust" (1560s); from dust (n.). Related: Dusted; dusting. Sense of "to kill" is U.S. slang first recorded 1938 (compare bite the dust under bite (v.)).