The correct spelling of the word "Alacrious" should actually be "Alacritous" (/əˈlæk.rə.təs/). This word means "brisk and cheerful readiness" and is derived from Latin "alacritās". The phonetic transcription of the correct spelling shows that the stress falls on the second syllable and the vowel sound is pronounced as "æ" (as in "cat"). It's important to use the correct spelling and pronunciation of words not only to communicate effectively but also to display a high level of proficiency in the language.
The word "alacrious" does not have an established etymology, as it is not a widely recognized or commonly used term in English. It is possible that "alacrious" is a variation or misspelling of the word "alacrity", which refers to a state of eagerness, promptness, or liveliness. The term "alacrity" comes from the Latin word "alacritas", meaning "liveliness" or "eagerness", which is derived from the adjective "alacer", meaning "lively" or "brisk". However, it is important to note that "alacrious" is not a standard or recognized English word.