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.)).