Etymology
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Words related to active

*ag- 

Proto-Indo-European root meaning "to drive, draw out or forth, move."

It forms all or part of: act; action; active; actor; actual; actuary; actuate; agency; agenda; agent; agile; agitation; agony; ambagious; ambassador; ambiguous; anagogical; antagonize; apagoge; assay; Auriga; auto-da-fe; axiom; cache; castigate; coagulate; cogent; cogitation; counteract; demagogue; embassy; epact; essay; exact; exacta; examine; exigency; exiguous; fumigation; glucagon; hypnagogic; interact; intransigent; isagoge; litigate; litigation; mitigate; mystagogue; navigate; objurgate; pedagogue; plutogogue; prodigal; protagonist; purge; react; redact; retroactive; squat; strategy; synagogue; transact; transaction; variegate.

It is the hypothetical source of/evidence for its existence is provided by: Greek agein "to lead, guide, drive, carry off," agon "assembly, contest in the games," agōgos "leader," axios "worth, worthy, weighing as much;" Sanskrit ajati "drives," ajirah "moving, active;" Latin actus "a doing; a driving, impulse, a setting in motion; a part in a play;" agere "to set in motion, drive, drive forward," hence "to do, perform," agilis "nimble, quick;" Old Norse aka "to drive;" Middle Irish ag "battle."

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activate (v.)
1620s, "make active, intensify;" see active + -ate (2). Meaning "put into action" is from 1902, originally in chemistry. Related: Activated; activating.
actively (adv.)
c. 1400, "secularly," from active + -ly (2). Meaning "vigorously" is early 15c.
activeness (n.)
c. 1600, from active + -ness.
activism (n.)
1920 in the political sense of "advocating energetic action;" see active + -ism. Earlier (1907) it was used in reference to a philosophical theory. Compare activist.
activist (n.)
"one who advocates a doctrine of direct action" in any sense, 1915; from active + -ist. Originally in reference to a political movement in Sweden advocating abandonment of neutrality in World War I and active support for the Central Powers. The word was used earlier in philosophy (1907).
activity (n.)
c. 1400, "active or secular life," from Old French activité, from Medieval Latin activitatem (nominative activitas), a word in Scholastic philosophy, from Latin activus "active" (see active). Meaning "state of being active, briskness, liveliness" recorded from 1520s; that of "capacity for acting on matter" is from 1540s. As "an educational exercise," 1923.
hyperactive (adj.)
1852, from hyper- "over, exceedingly, to excess" + active.
inactive (adj.)

"not active or acting," 1640s, from in- (1) "not, opposite of" + active. Perhaps a back-formation from inactivity.

interactive (adj.)
"acting upon or influencing each other," 1832, from interact (v.), probably on model of active. Related: Interactively; interactivity.