The question I asked was disputed amongst XVIIe century physicists ( at least before the invention of calculus). 

How is it solved by modern physics? 


If the object is at rest at some instant , one cannot understand how the movement starts again ( due to the inertia principle). 

If the object is not at rest at some instant, it seems necesssary that there is some instant at which it goes in both directions ( for example , some moment at which a ball bouncing on the ground is both falling and going back up). 

In which false assumptions does this dilemma originate according to modern physics?