Force, Work, and Energy

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What do you want? An hypothetical example is full of assumptions. If you want a true example get two objects and make them collide and take note of their speeds before and after...
Reality is between the two extreme cases of perfect elastic and perfect inelastic. The world PERFECT should have already hinted at that.

Also pineapple at cinetic/kinetic, with 3 different languages to write this I never know which one it is.



For a more mathematical base: With the momentum equation you still have one degree of freedom in your system. So you decide how much of the kinetic energy is conservated, either all (perfect elastic) or minimum (perfect inelastic) or anything inbetween. That decision can be arbitrary or based on experiments (if you are simulating a real system and you have data that shows how "elastic" the collision is).