My confusion arises with free falling body.
For a free falling body the displacement ~ time graph has a kink (at the time when the body hit the ground ). at a kink point, a function is not derivable by the rule of calculus. but we see in the free falling case the body has velocity but in opposite direction at the moment it hit the ground.
- For same free falling body as the velocity is a discontinuous function of time (at the time when it hit the ground) there should not be any acceleration because a derivative function must be continuous by the theory of calculus. But velocity $v$ is not continuous at that moment of time (when it hits the ground). But it has an acceleration spike value. So I'm confused very much with this mismatch with mathematical theorem and the practical application in physics. what is the solution??