Etymology
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impetus (n.)

early 15c., impetous "rapid movement, rush;" 1640s, with modern spelling, "force with which a body moves, driving force," from Latin impetus "an attack, assault; rapid motion; an impulse; violence, vigor, force;" figuratively "ardor, passion," from impetere "to attack," from assimilated form of in- "into, in, on, upon" (from PIE root *en "in") + petere "aim for, rush at" (from PIE root *pet- "to rush, to fly").

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impetigo (n.)
pustular disease of the skin, late 14c., from Latin impetigo "skin eruption," from impetere "to attack" (see impetus). Originally used generally; the sense narrowed in modern times to specific diseases. Related: Impetiginous.
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impetuous (adj.)
late 14c., "hot-tempered, fierce;" late 15c., "done or given with a rush of force," from Old French impetuos (13c., Modern French impétueux) and directly from Late Latin impetuosus "impetuous, violent" (source also of Spanish and Italian impetuoso), from Latin impetus "attack" (see impetus). Related: Impetuously; impetuousness.
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impeach (v.)

formerly also empeach, late 14c., empechen, "to impede, hinder, prevent;" early 15c., "cause to be stuck, run (a ship) aground," also "prevent (from doing something)," from Anglo-French empecher, Old French empeechier "to hinder, stop, impede; capture, trap, ensnare" (12c., Modern French empêcher), from Late Latin impedicare "to fetter, catch, entangle," from assimilated form of in- "into, in" (from PIE root *en "in") + Latin pedica "a shackle, fetter," from pes (genitive pedis) "foot" (from PIE root *ped- "foot").

In law, at first in a broad sense, "to accuse, bring charges against" from late 14c.; more specifically, of the king or the House of Commons, "to bring formal accusation of treason or other high crime against (someone)" from mid-15c.  The sense of "accuse a public officer of misconduct" had emerged from this by 1560s. The sense shift is perhaps via Medieval Latin confusion of impedicare with Latin impetere "attack, accuse" (see impetus), which is from the Latin verb petere "aim for, rush at" (from PIE root *pet- "to rush, to fly").

The Middle English verb apechen, probably from an Anglo-French variant of the source of impeach, was used from early 14c. in the sense "to accuse (someone), to charge (someone with an offense)." Related: Impeached; impeaching.

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*pet- 

Also petə-, Proto-Indo-European root meaning "to rush, to fly." 

It forms all or part of: accipiter; appetence; appetite; apterous; apteryx; archaeopteryx; asymptote; centripetal; Coleoptera; compete; competent; eurypterid; feather; helicopter; hippopotamus; Hymenoptera; impetigo; impetuous; impetus; iopterous; Lepidoptera; ornithopter; panache; panne; pen (n.1) "writing implement;" pennon; peripeteia; perpetual; perpetuity; petition; petulance; petulant; pin; pinion; pinnacle; pinnate; pinniped; potamo-; potamology; propitiation; propitious; ptero-; pterodactyl; ptomaine; ptosis; repeat; symptom.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit pattram "wing, feather, leaf," patara- "flying, fleeting;" Hittite pittar "wing;" Greek piptein "to fall," potamos "river, rushing water," pteron, pteryx "feather, wing," ptilon "soft feathers, down, plume;" Latin petere "to attack, assail; seek, strive after; ask for, beg; demand, require," penna "feather, wing;" Old Norse fjöðr, Old English feðer "feather;" Old Church Slavonic pero "feather;" Old Welsh eterin "bird."

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*en 
Proto-Indo-European root meaning "in."

It forms all or part of: and; atoll; dysentery; embargo; embarrass; embryo; empire; employ; en- (1) "in; into;" en- (2) "near, at, in, on, within;" enclave; endo-; enema; engine; enoptomancy; enter; enteric; enteritis; entero-; entice; ento-; entrails; envoy; envy; episode; esoteric; imbroglio; immolate; immure; impede; impend; impetus; important; impostor; impresario; impromptu; in; in- (2) "into, in, on, upon;" inchoate; incite; increase; inculcate; incumbent; industry; indigence; inflict; ingenuous; ingest; inly; inmost; inn; innate; inner; innuendo; inoculate; insignia; instant; intaglio; inter-; interim; interior; intern; internal; intestine; intimate (adj.) "closely acquainted, very familiar;" intra-; intricate; intrinsic; intro-; introduce; introduction; introit; introspect; invert; mesentery.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit antara- "interior;" Greek en "in," eis "into," endon "within;" Latin in "in, into," intro "inward," intra "inside, within;" Old Irish in, Welsh yn, Old Church Slavonic on-, Old English in "in, into," inne "within, inside."
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elan (n.)
"vivacity," 1877, from French élan (16c.), "spring, bound, impetus," noun derived from élancer "to shoot, incite" (trans.); "rush forward, dart" (intrans.), from Old French elancer, from e- "out" (see ex-) + lancer "to throw," originally "to throw a lance," from Late Latin lanceare, from Latin lancea (see lance (n.)).
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whip (v.)

mid-13c., wippen "flap violently," not in Old English, of uncertain origin, ultimately from Proto-Germanic *wipjan "to move back and forth" (source also of Danish vippe "to raise with a swipe," Middle Dutch, Dutch wippen "to swing," Old High German wipf "swing, impetus"), from PIE root *weip- "to turn, vacillate, tremble." "The senses of both [noun and verb] no doubt represent several independent adoptions or formations" [OED]. The cookery sense is from 1670s. Related: Whipped; whipping. Whip snake first recorded 1774, so called for its shape.

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local (adj.)

late 14c., "pertaining to position," originally medical: "confined to a particular part of the body;" from Old French local "local" (13c.) and directly from Late Latin localis "pertaining to a place," from Latin locus "a place, spot" (see locus).

The meaning "limited to a particular place" is from c. 1500. Local color is from 1721, originally a term in painting; the meaning "anything picturesque" is from c. 1900. Local option (1868, American English) is from the prohibition movement: "the right of a community to vote on whether to allow the sale of intoxicating liquor there." Local talent "attractive women thereabouts" is from 1947 in UK slang; earlier it was used in reference to entertainment acts in shows, radio broadcast, etc.

Thus, with the local talent, we have many factors which help "sell" is in quantities far beyond what the commercial market would carry. Pride in children, interest in relatives and friends, and pride in locality all give impetus to the development of home talent. [Horace Boies Hawthorn, "The Sociology of Rural Life," 1926]
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coast (v.)

late 14c., "to skirt, to go around the sides, to go along the border" of something (as a ship does the coastline), from Anglo-French costien, from the French source of coast (n.).

The meaning "sled downhill," first attested 1834 in American English, is a separate borrowing or a new development from the noun. In bicycle-riding, "descend a hill with the feet off the pedals," from 1879. Of motor vehicles, "to move without thrust from the engine," from 1896; figurative use, of persons, "not to exert oneself," by 1934. Related: Coasted; coasting.

"Coasting" consists in throwing the legs up over the handles and allowing the bicycle to rush of its own impetus down hill. It can only be done with safety where the road is perfectly smooth, hard, and free from obstructions; but, under such conditions, bicycle coasting affords one of the most glorious and exhilarating of sensations, and, next to ballooning, its motion most nearly resembles the flight of a bird. [Harper's Weekly, Dec. 20, 1879]
The reckless coasting down the long hills on the route was scarcely more defensible. Speeds of 25 to 30 miles an hour were reached in some instances. The common road is not the proper place for such exhibitions, especially in populous centres. The risk is altogether too great, both for occupants of the vehicle and for other frequenters of the highway. [account of an automobile race on the streets of New York in The Horseless Age, June 1896] 
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