повільний

From по- (po-) +‎ воля (volja) +‎ -ний (-nyj). Compare with Polish powolny, Belarusian павольны (pavólʹny), and Czech pozvolný (“gradual”).

You can also compare the prefix по- (po-) in this context with Slovak pomalý (“slow”) from po- + malý (“small”), with Serbo-Croatian polagan (“slow, gradual”) from po- + lagan (“light, lightweight; easy”), with Macedonian полека (poleka, “slowly”) from по- (po-) + лек (lek, “light, lightweight”), with Slovene počasen (“slow”) from po- + čas (“time”) + -en, with Russian постепенный (postepennyj, “gradual”) from по- (po-) + степень (stepenʹ) + -ный (-nyj), and with Ukrainian поступовий (postupovyj, “gradual, slow”) from по- (po-) + ступати (stupaty, “to step, to tread”) + -овий (-ovyj).

Ukrainian вільний (vilʹnyj) does not have a meaning of "slow" on its own like Polish wolny does. However, comparing the meaning of the cognates of Ukrainian вільний (vilʹnyj) from Proto-Slavic *volьnъ in other Slavic languages, we can assume that the meaning of "slow" in Polish wolny is most likely derivative from Polish powolny. However, Ukrainian вільний (vilʹnyj) has the additional meaning of "light, easy"^[1] that can be compared with the already mentioned terms Serbo-Croatian polagan and Macedonian полека (poleka), which contain a partial meaning of "light". Similarities can also be seen in Ukrainian легенький (lehenʹkyj, “light; slow, gradual”)^[2] and Ukrainian поле́гом (poléhom, “slowly, not in a hurry”)^[3] which are both formed from Ukrainian легкий (lehkyj, “light; easy”).

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пові́льний • (povílʹnyj) (comparative пові́льніший, superlative найпові́льніший, adverb пові́льно)

1. slow

   Antonyms: швидки́й (švydkýj), ско́рий (skóryj), би́стрий (býstryj), жва́вий (žvávyj), спри́тний (sprýtnyj), прудки́й (prudkýj)

2. lasting, long
3. gradual

   Synonyms: поступо́вий (postupóvyj), поло́жистий (polóžystyj), поло́гий (polóhyj), спа́дистий (spádystyj), помі́рний (pomírnyj)

4. light, easy
5. (archaic) calm

• Melnychuk, O. S., editor (1982–2012), “повільний”, in Етимологічний словник української мови [Etymological Dictionary of the Ukrainian Language] (in Ukrainian), Kyiv: Naukova Dumka
• Bilodid, I. K., editor (1970–1980), “повільний”, in Словник української мови: в 11 т. [Dictionary of the Ukrainian Language: in 11 vols] (in Ukrainian), Kyiv: Naukova Dumka
• “повільний”, in Горох – Словозміна (in Ukrainian)