run-time n.

Old English, "move swiftly by using the legs, go on legs more rapidly than walking," also "make haste, hurry; be active, pursue or follow a course," and, of inanimate things, "to move over a course."

The modern verb is a merger of two related Old English words, in both of which the initial two letters sometimes switched places. The first is intransitive rinnan, irnan "to run, flow, run together" (past tense ran, past participle runnen), which is cognate with Middle Dutch runnen, Old Saxon, Old High German, Gothic rinnan, German rinnen "to flow, run."

The second is Old English transitive weak verb ærnan, earnan "ride, run to, reach, gain by running" (probably a metathesis of *rennan), from Proto-Germanic *rannjanan, causative of the root *ren- "to run." This is cognate with Old Saxon renian, Old High German rennen, German rennen, Gothic rannjan.

Watkins says both are from PIE *ri-ne-a-, nasalized form of root *rei- "to run, flow," but Boutkan's sources find this derivation doubtful based on the poor attestation of supposed related forms, and he lists it as of "No certain IE etymology."

Of streams, etc., "to flow," from late Old English. From c. 1200 as "take flight, retreat hurriedly or secretly." Phrase run for it "take flight" is attested from 1640s.

Also from c. 1200 as "compete in a race." Extended to "strive for any ends," especially "enter a contest for office or honors, stand as a candidate in an election" (1826, American English).

Of any sort of hurried travel, c. 1300. From early 13c. as "have a certain direction or course." By c. 1300 as "keep going, extend through a period of time, remain in existence." Specifically of theater plays by 1808. Of conveyances, stage lines, etc., "perform a regular passage from place to place" by 1817.

Of machinery or mechanical devices, "go through normal or allotted movements or operation," 1560s. Of colors, "to spread in a fabric when exposed to moisture," 1771. Of movie film, "pass between spools," hence "be shown," by 1931.

The meaning "carry on" (a business, etc.) is by 1861, American English; hence extended senses of "look after, manage." As "publish or print in a newspaper or magazine," by 1884. 

Many senses are via the notion of "pass into or out of a certain state." To run dry "cease to yield water or milk" (1630s). In commerce, "be of a specified price, size, etc.," by 1762. To run low "be nearly exhausted" is by 1712; to run short "exhaust one's supply" is from 1752; to run out of in the same sense is from 1713. To run on "keep on, continue without pause or change" is from 1590s.

The transitive sense of "cause to run" was in Old English. By late 15c. as "to pierce, stab," hence 1520s as "thrust through or into something." The meaning "enter (a horse) in a race" is from 1750. The sense of "cause a mechanical device to keep moving or working" is by 1817.

Many figurative uses are from horseracing or hunting (such as to run (something) into the ground "carry to excess, exhaust by constant pursuit," 1836, American English).

To run across "meet by chance, fall in with" is attested from 1855, American English. To run into in this sense is by 1902. To run around with "consort with" is from 1887.

In reference to fevers by 1918. To run a (red) traffic signal is by 1933. Of tests, experiments, etc., by 1947. Of computers by 1952. Time has been running out since c. 1300. To run in the family is by 1771. The figurative expression run interference (1929) is from U.S. football. To run late is from 1954.

Old English tima "limited space of time," from Proto-Germanic *timon- "time" (source also of Old Norse timi "time, proper time," Swedish timme "an hour"), from PIE *di-mon-, suffixed form of root *da- "to divide."

Abstract sense of "time as an indefinite continuous duration" is recorded from late 14c. Personified at least since 1509 as an aged bald man (but with a forelock) carrying a scythe and an hour-glass. In English, a single word encompasses time as "extent" and "point" (French temps/fois, German zeit/mal) as well as "hour" (as in "what time is it?" compare French heure, German Uhr). Extended senses such as "occasion," "the right time," "leisure," or times (v.) "multiplied by" developed in Old and Middle English, probably as a natural outgrowth of such phrases as "He commends her a hundred times to God" (Old French La comande a Deu cent foiz).

to have a good time ( = a time of enjoyment) was common in Eng. from c 1520 to c 1688; it was app. retained in America, whence readopted in Britain in 19th c. [OED]

Time of day (now mainly preserved in negation, i.e. what someone won't give you if he doesn't like you) was a popular 17c. salutation (as in "Good time of day vnto your Royall Grace," "Richard III," I.iii.18), hence to give (one) the time of day "greet socially" (1590s); earlier was give good day (mid-14c.).

The times "the current age" is from 1590s. Behind the times "old-fashioned" is recorded from 1831. Times as the name of a newspaper dates from 1788. To be ahead of (one's) time is by 1837.

Time warp is attested by 1954; time-traveling in the science fiction sense is by 1895 in H.G. Wells' "The Time Machine." Time capsule is attested from 1938, in reference to the one "deemed capable of resisting the effects of time for five thousand years preserving an account of universal achievements embedded in the grounds of the New York World's fair."

Jones [archaeologist of A.D. 5139] potters about for a while in the region which we have come to regard as New York, finds countless ruins, but little of interest to the historian except a calcified direction sheet to something called a "Time Capsule." Jones finds the capsule but cannot open it, and decides, after considerable prying at the lid, that it is merely evidence of an archaic tribal ceremony called a "publicity gag" of which he has already found many examples. [Princeton Alumni Weekly, April 14, 1939]

To do time "serve a prison sentence" is from 1865. Time frame is attested by 1964; time-limit is from 1880. About time, ironically for "long past due time," is recorded from 1920. To be on time is by 1854 in railroading.