This paradox is a popular one that seems to have no resolution since the existence of one seems to deny the possibility of the other. After all, if you have an unstoppable force that must mean that there can be no such thing as immovable object and vice versa.
But while one can dismiss the paradox on those grounds, it is interesting to look more closely at it to try and get a better understanding of what we mean when we say ‘unstoppable’ and ‘immovable’ and try to give operational, as opposed to intuitive, meanings to those words. In doing so, we usually arrive at a deeper understanding of the paradox and of relevant physics principles.
Via Maggie Koerth-Baker I came across this interesting video that does just that.