**Question.** If we just consider a one-dimensional collision between two objects (ignore friction as well), Newton's law of restitution states that the speed of separation after the collision divided by the speed of approaching before the collision gives the coefficient of restitution, say $e$, whose value is inclusively between 0 and 1. My question is how this can be proved.

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**My Thought.** Generally I have no idea how to come out with a proof. Nevertheless, I am thinking about a specific scenario in which object $A$ with mass $m\_1$ and speed $v\_1$ is hitting object $B$ with mass $m\_2$ and zero speed, and after the collision object $A$ stops and object $B$ has speed $v\_2$. Now if we suppose there is no loss in kinetic energy during the collision (so elastic collision), and $m\_1>m\_2$, then it is clear $v\_2>v\_1$. But $v\_2$ is the separation speed while $v\_1$ is the approaching speed, and this leads to an $e$ which exceeds $1$, contradicting Newton's law of restitution. If the law is correct, then this cannot happen, but why it can't?

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**Comment.** Any kind of help including brief hints and formal answers are welcome and will be appreciated.