And so by definition , the thing force is the end product of accelerating masses. And more to the point, defining a property force in this way, in concert with a system of other relations, allows you to solve problems you care about. But a relation between force, mass and acceleration isn't going to get us very far. And the reason for this is the nature of the problem presented. This problem provides us little information other than the fact that it is a closed event.
Objects are moving, they collide and they move apart.
However such a closed system of moving objects is the hallmark of the application of conservation principles. Unfortunately for purposes of our problem there is no conservation law for force. By conservation we mean a law which provides under certain circumstances that a given quality must remain unchanged through the process that is the problem at hand. However, this is not how the concepts actually arise in physics. This is our relation for momentum.