mid-15c., cohercen, "restrain or constrain by force of law or authority," from Old French cohercier, from Latin coercere "to control, restrain, shut up together," from assimilated form of com- "together" (see co-) + arcere "to enclose, confine, contain, ward off," from PIE *ark- "to hold, contain, guard" (see arcane). The unetymological -h- was perhaps by influence of cohere. Related: Coerced; coercing. No record of the word between late 15c. and mid-17c.; its reappearance 1650s is perhaps a back-formation from coercion.
word-forming element making adjectives from verbs, meaning "pertaining to, tending to; doing, serving to do," in some cases from Old French -if, but usually directly from Latin adjectival suffix -ivus (source also of Italian and Spanish -ivo). In some words borrowed from French at an early date it has been reduced to -y (as in hasty, tardy).
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<a href="https://www.etymonline.com/word/coercive">Etymology of coercive by etymonline</a>
Harper, D. (n.d.). Etymology of coercive. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/coercive