Etymology
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rapidity (n.)

"celerity of motion or action," 1650s, from French rapidité and directly from Latin rapiditatem (nominative rapiditas) "swiftness, rapidity, velocity," from rapidus "hasty, swift, rapid" (see rapid).

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quickness (n.)

c. 1200, quiknesse, "state of being alive," from quick (adj.) + -ness. Early 15c. as "alacrity, speed, rapidity;" mid-15c. as "readiness of perception, keenness of mind."

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celerity (n.)

"swiftness, rapidity of motion," late 15c., from Old French celeritee (14c., Modern French célérité), from Latin celeritatem (nominative celeritas) "swiftness," from celer "swift," from PIE *keli- "speeding" (source also of Sanskrit carati "goes," Greek keles "fast horse or ship," Lithuanian šuoliai "a gallop," Old High German scelo "stallion").

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Pilate (n.)

late 14c. as a term of reproach for a corrupt or lax prelate, from the Roman surname, especially that of Pontius Pilate, a governor of the Roman province of Judaea under Tiberius, from Latin Pilatus, literally "armed with javelins," from pilum "javelin" (see pile (n.2)).

Other than having presided over the trial of Jesus and ordering his crucifixion, little is known of him. In Middle English pilates vois was "a loud, boastful voice," of the sort used by Pilate in the mystery plays. Among slang and cant uses of Pontius Pilate mentioned in the 1811 "Dictionary of Buckish Slang, University Wit and Pickpocket Eloquence" is "(Cambridge) a Mr. Shepherd of Trinity College; who disputing with a brother parson on the comparative rapidity with which they read the liturgy, offered to give him as far as Pontius Pilate in the Belief."

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pitch (n.1)

1520s, "something that is thrust in or fixed or pierced," from pitch (v.1). Sense of "slope, degree, inclination" is from 1540s; from 1550s as "highest point or reach;" from 1620s as "height" in general. Meaning "height of an arched roof above the floor" is by 1610s.

Meaning "a throw, a toss, an act of throwing" is attested by 1833. Meaning "act of plunging headfirst" is from 1762. The musical sense of "characteristic of a sound or tone that depends upon relative rapidity of vibration" is from 1590s, also "particular tonal standard." See pitch (v.1) for sense evolutions, but the connection of many of these is obscure.

Some noun senses are from the older sense of pitch as "to thrust in, drive (a stake)." Thus, in cricket, "place where the wickets are pitched" (1871).

Sales pitch in the modern commercial advertising sense is from 1943, American English; pitch in the sense of "tedious or inflated sales talk" is attested by 1876, perhaps ultimately from the baseball sense. Pitch also was "place on which to pitch or set up a booth for sale or exhibition" (by 1851).

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speed (n.)

Old English sped "success, a successful course; prosperity, riches, wealth; luck; opportunity, advancement," from Proto-Germanic *spodiz (source also of Old Saxon spod "success," Dutch spoed "haste, speed," Old High German spuot "success," Old Saxon spodian "to cause to succeed," Middle Dutch spoeden, Old High German spuoten "to haste"), from PIE *spo-ti-, from root *spes- or *speh- "prosperity" (source also of Hittite išpai- "get full, be satiated;" Sanskrit sphira "fat," sphayate "increases;" Latin spes "hope," sperare "to hope;" Old Church Slavonic spechu "endeavor," spĕti "to succeed," Russian spet' "to ripen;" Lithuanian spėju, spėti "to have leisure;" Old English spōwan "to prosper").

Meaning "rapidity of movement, quickness, swiftness" emerged in late Old English (at first usually adverbially, in dative plural, as in spedum feran). Meaning "rate of motion or progress" (whether fast or slow) is from c. 1200. Meaning "gear of a machine" is attested from 1866. Meaning "methamphetamine, or a related drug," first attested 1967, from its effect on users.

Speed limit is from 1879 (originally of locomotives); speed-trap is from 1908. Speed bump is 1975; figurative sense is 1990s. Full speed is recorded from late 14c. Speed reading first attested 1965. Speedball "mix of cocaine and morphine or heroin" is recorded from 1909.

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cut (v.)

c. 1300, "to make, with an edged tool or instrument, an incision in; make incisions for the purpose of dividing into two or more parts; remove by means of a cutting instrument;" of an implement, "have a cutting edge," according to Middle English Compendium from a presumed Old English *cyttan, "since ME has the normal regional variants of the vowel." Others suggest a possible Scandinavian etymology from North Germanic *kut- (source also of Swedish dialectal kuta "to cut," kuta "knife," Old Norse kuti "knife"), or that it is from Old French couteau "knife."

It has largely displaced Old English ceorfan (see carve (v.)), snian, and scieran (see shear). The past participle is also cut, though cutted sometimes has been used since Middle English.

From early 14c. as "to make or fashion by cutting or carving." From c. 1400 as "to intersect or cross." From early 15c. as "abridge or shorten by omitting a part."

Meaning "to wound the sensibilities of" is from 1580s (to cut the heart in the same sense is attested from early 14c.). Sense of "sever connection or relations with" is from 1630s.

Meaning "to be absent without excuse" is British university slang from 1794. Colloquial or slang sense of "move off with directness and rapidity" is from 1580s. Meaning "divide (a deck of cards) at random into parts before the deal" to prevent cheating is from 1530s.

Meaning "to dilute, adulterate" (liquor, etc.) is by 1930. Colloquial sense of "to divide or share" is by 1928, perhaps an image from meat-carving at table. As a director's call to halt recording or performing, by 1931 (in an article about Pete, the bulldog with the black-ringed eye in the Hal Roach studios shorts, who was said to know the word). The sense of "perform, execute" (c. 1600) is in cut capers "frisk about;" cut a dash "make a display."

To cut down is from late 14c. as "to fell;" by 1821 as "to slay" (as with a sword); 1857 as "to curtail." To cut (someone or something) down to size is from 1821 as "reduce to suitable dimensions;" the figurative sense, "reduce to the proper level of importance," is by 1927.

To cut in "enter suddenly and unceremoniously" is from 1610s; sense of "suddenly join in conversation, interrupt" is by 1830. To cut up "cut in pieces" is from 1570s. To cut back is from 1871 as "prune by cutting off shoots," 1913 in cinematography, "return to a previous scene by repeating a part of it," 1943 as "reduce, decrease" (of expenditures, etc.). To cut (something) short "abridge, curtail, interrupt" is from 1540s.

In nautical use to cut a feather (1620s) is to move so fast as to make water foam under the bow. To cut and run (1704) also is originally nautical, "cut cable and set sail immediately," as in an emergency, hence, generally, "to make off suddenly."

To cut the teeth "have the teeth grow through the gums" as an infant is from 1670s. To cut both ways in the figurative sense of "have a good and bad effect" is from c. 1600. To cut loose "set (something) free" is by 1828; intransitive sense "begin to act freely" is by 1909.

Cut it out "remove (something) by or as if by cutting" yielded a figurative use in the command cut it out! "Stop! That's enough!" by 1933. The evolution seems to have begun earlier. A piece attributed to the Chicago Live Stock World that made the rounds in trade publications 1901-02 begins:

When you get 'hot' about something and vow you are going to rip something or somebody up the back—cut it out.
If you feel disposed to try the plan of building yourself up by tearing some one else down—cut it out.

Playing on both senses, it ends with "Should you, after reading this preachy stuff, fear you might forget some of the good advice—cut it out."

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