The word vehemently has a lot of force behind it. It traces back to the Latin word vehement, meaning “impetuous, violent.” If you do something vehemently, then you do it forcefully and with emotion, and no one will doubt how you really feel. You’ll often hear it used to describe situations involving conflict or disagreement. If you vehemently deny your involvement in the incident with the lawnmower, then you deny it very strongly.