Something that behaves inexorably is unmovable, not persuadable, or relentless: like your heart beating inexorably as the rollercoaster climbs inexorably up the hill.
Like a runner heading toward the finish line or a story spiraling to an end, the adverb inexorably is for things that have momentum and just keep going. A boulder falling down a mountain is moving inexorably. If you fail class after class, you're moving inexorably toward flunking out of school. People are always aging, and we're all moving inexorably (though slowly) toward death. This is a strong word for powerful events and forces that just won't stop.