Etymology
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Words related to motive

*meue- 
*meuə-, Proto-Indo-European root meaning "to push away."

It forms all or part of: commotion; emotion; mob; mobile; moment; momentary; momentous; momentum; motif; motility; motion; motive; moto-; motor; move; movement; mutiny; premotion; promote; remote; remove.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit kama-muta "moved by love" and probably mivati "pushes, moves;" Greek ameusasthai "to surpass," amyno "push away;" Latin movere "move, set in motion;" Lithuanian mauti "push on."
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leitmotif (n.)
also leitmotiv, "a musical figure to which some definite meaning is attached," 1876, from German Leitmotiv, literally "leading motive," from leiten "to lead" (see lead (v.1)) + Motiv (see motive). A term associated with Wagnerian musical drama, though the thing itself is at least as old as Mozart. "The leitmotif must be characteristic of the person or thing it is intended to represent." ["Elson's Music Dictionary"]
locomotive (adj.)
1610s, "pertaining to movement," from French locomotif, from Latin loco "from a place" (ablative of locus "place;" see locus) + Late Latin motivus "moving" (see motive).

From 1650s as "moving from place to place;" by 1814 as "having the power of moving by itself. The noun meaning "engine which travels on rails by its own power" is from 1829, short for locomotive engine, which is attested from 1814. A locomotive engine used without rails was a traction engine, which became tractor.
motif (n.)

"theme, predominant feature that recurs often in an artistic or dramatic work," 1848, from French motif "dominant idea, theme," from Medieval Latin motivus "moving, impelling," from past participle stem of movere "to move" (from PIE root *meue- "to push away"). Also a Middle English form of motive (late 14c.).

motivate (v.)

"to stimulate toward action, act as the inciting cause of," 1863, from motive + -ate (2); perhaps modeled on French motiver or German motivieren. Related: Motivated; motivating.

motiveless (adj.)

"having no motive or aim," 1798, from motive (n.) + -less.

automotive (adj.)
"pertaining to automobiles," 1898, a hybrid from auto- "self," from Greek, and motive (adj.), from Latin. Used earlier as a noun (1865) in reference to some sort of helicopter-like device.