Sentir comes from the Latin for the same, sentire, which in turn comes from the Proto-Indo-European root *sent, meaning, “to go” — feels are thus, definitionally, fleeting, things that come and go.
From the Latin sentire, we get a bunch of similar words in English, including:
And a few others, including assent, consent, dissent and, most obviously, sentiment.
From the original Proto-Indo-European root *sent, meaning “to go” — via German, that turned into some simpler English words that we can now consider distant cousins of Sentir: send. Feelings do come and go!