onrush (n.)

"in a position above and in contact with; in such a position as to be supported by;" also noting the goal to which some action is or has been directed; "about, concerning, regarding; in a position to cover;" as an adverb, "in or into a position in contact with and supported by the top or upper part of something; in or into place; in place for use or action; into movement or action; in operation," Old English on, unstressed variant of an "in, on, into," from Proto-Germanic *ana "on" (source also of Dutch aan, German an, Gothic ana "on, upon"), from PIE root *an- (1) "on" (source also of Avestan ana "on," Greek ana "on, upon," Latin an-, Old Church Slavonic na, Lithuanian nuo "down from").

Also used in Old English in many places where we now would use in. From 16c.-18c. (and still in northern England dialect) often reduced to o'. Phrase on to "aware" is from 1877.

mid-14c. (implied in rushing), "to drive back or down," from Anglo-French russher, from Old French ruser "to dodge, repel," which is from Latin recusare"make an objection against; decline, refuse, reject; be reluctant to" (see recuse; also compare ruse).

The meaning "do something quickly" is from 1650s, hence "to move or act with undue eagerness or without deliberation or preparation;" the transitive sense of "to hurry up (someone or something), cause to go swiftly" is from 1850. The sporting sense in U.S. football originally was in rugby (1857).

The fraternity/sorority sense is by 1896 (originally it was what the fraternity did to the student); from 1899 as a noun in this sense, "entertainment for prospective pledges." Earlier it was a name on U.S. campuses for tests of strength or athletic skill between freshmen and sophomores as classes (1860).