Is it allowed to use the word "one's" in academic writing?
For example: It can help improve one's vocabulary.
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It's acceptable, but "one" is, in general, less commonly used as a pronoun than it would be in, say, French (bonjour, mademoiselle). "One" tends to somewhat imply the second-person "you," because it is a much more common construction in English. So as an American, "It can help improve one's vocabulary" sounds a bit prescriptive, like something I should do personally. I mentally translate it as "It can help improve your vocabulary."
Academic writing tends to favor pure third person if it is possible, like "It can help improve the vocabulary of persons participating in the activity."