"move rapidly," 1852, of echoic origin. Related: Zipped; zipping. Zip gun "homemade pistol" first recorded 1950.
"to close or fasten by means of a zipper," 1932, back-formation from zipper. Related: Zipped; zipping.
"zero," 1900, student slang for a grade of zero on a test, etc.; of unknown origin; cf. zilch.
1963, in U.S. postal ZIP code, an acronym for Zone Improvement Plan, no doubt chosen with conscious echo of zip (v.1).
not give a damn, not know beans
[1900+ Students; like zilch, probably coined from a familiar word beginning with z]