Is the coefficient of restitution negative? I recently came across a formula for the coefficient of restitution:

Why is there a negative sign?
 A: This expanation deals with objects that do not pass through one another. 
Firstly replace the bars with brackets to make the formula correct. If you don't, it becomes wrong because of the little negative sign.
The coefficient of restitution is a number with a value that lies in the range of 0 to 1. It can never be negative.
If the formular is presented in that form, the denominator represents the relative "velocity" of approach and the numerator (excluding the negative sign) represents the relative "velocity" of separation.
Now since one object is always chosen as the frame of reference of the other, either of the two (i.e relative velocity of approach/relative velocity of separation) can have a negative sign as a consequence of calculation, not both.
NB: the negative sign i'm refering to in the last statement isn't the one in the equation. It's actually a result of calculating.
The negative sign in the equation is put in order create some sought of a sign balance. Let's say e=1 , equating the denominator to the numerator without the negative sign wouldn't be right since we mentioned that either one is always negative ( due to the approach and separation of an object with our reference frame) so in order to compansate for that we have to plug in a negative sign to the formula at the correct side. Which is the one shown above.
Feel free to correct me, i'm just a learner after all.
Hope this helped a bit.
