In a sharp, severe, or intense way; with a keen or sensitive awareness.
From Latin 'acutus' (sharp, pointed), combined with '-ly.' The word originally referred to pointed or sharp objects before extending to describing intense feelings or perceptions.
Acutely comes from the same Latin root as 'acute angle'—a sharp angle less than 90 degrees—so when you feel something 'acutely,' it's like an emotional sharp point piercing your awareness, which is why psychological pain that's acute is almost worse than dull chronic pain.
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