Etymology
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finish (v.)
late 14c., "to bring to an end;" mid-15c., "to come to an end" (intransitive), from Old French finiss-, present participle stem of fenir "stop, finish, come to an end; die" (13c.), from Latin finire "to limit, set bounds; put an end to; come to an end," from finis "that which divides, a boundary, border," figuratively "a limit, an end, close, conclusion; an extremity, highest point; greatest degree," which is of unknown origin, perhaps related to figere "to fasten, fix" (see fix (v.)). Meaning "to kill, terminate the existence of" is from 1755.
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finish (n.)
1779, "that which finishes or gives completion," from finish (v.). Meaning "the end" is from 1790. Finish line attested from 1873.
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up (n.)
"that which is up," 1530s, from up (adv.). Phrase on the up-(and-up) "honest, straightforward" first attested 1863, American English.
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up (adv.)

Old English up, uppe, from Proto-Germanic *upp- "up" (source also of Old Frisian, Old Saxon up "up, upward," Old Norse upp; Danish, Dutch op; Old High German uf, German auf "up"; Gothic iup "up, upward," uf "on, upon, under;" Old High German oba, German ob "over, above, on, upon"), from PIE root *upo "under," also "up from under," hence also "over."

As a preposition, "to a higher place" from c. 1500; also "along, through" (1510s), "toward" (1590s). Often used elliptically for go up, come up, rise up, etc. Up the river "in jail" first recorded 1891, originally in reference to Sing Sing, which is up the Hudson from New York City. To drive someone up the wall (1951) is from the notion of the behavior of lunatics or caged animals. Insulting retort up yours (scil. ass) is attested by late 19c.

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up- 
prefix with various senses, from Old English up (adv.), corresponding to similar prefixes in other Germanic languages.
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up (v.)

1550s, "to drive and catch (swans)," from up (adv.). Intransitive meaning "get up, rise to one's feet" (as in up and leave) is recorded from 1640s. Sense of "to move upward" is recorded from 1737. Meaning "increase" (as in up the price of oil) is attested from 1915. Compare Old English verb uppian "to rise up, swell." Related: Upped; upping. Upping block, used for mounting or dismounting horses, carriages, etc., is attested from 1796 (earlier was horsing-block, 1660s).

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up (adj.)
c. 1300, "dwelling inland or upland," from up (adv.). Meaning "going up" is from 1784. From 1815 as "excited, exhilarated, happy," hence "enthusiastic, optimistic." Up-and-coming "promising" is from 1848. Musical up-tempo (adj.) is recorded from 1948.
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cover-up (n.)

also coverup, "means or act of concealing" some event or activity, 1922, from the verbal phrase (1872), from cover (v.) + up (adv.).

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pop-up (n.)
from 1906 as a type of baseball hit; from pop (v.) + up (adv.). As an adjective from 1934 (of a children's book, later toasters, etc.).
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shut up (v.)

c. 1400, "keep from view or use," from shut (v.) + up (adv.). Meaning "cause to stop talking" is from 1814; intransitive meaning "cease from speaking" is from 1840. Put up or shut up "defend yourself or be silent" is U.S. slang, by 1868.

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