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If one particle with mass m moving with velocity v has a perfectly inelastic collision with another particle of mass m at rest, then both will move together with the velocity v/2. According to the first definition, e = 0 as the final relative velocity is 0. However, according to the second definition, e = √((1/2(2m)(v/2)

^{2})/(1/2mv^2)) which is 1/√2.

Also, Wikipedia says that "A perfectly inelastic collision has a coefficient of 0, but a 0 value does not have to be perfectly inelastic.". Can someone give me an example of a collision with a coefficient of 0 that is not perfectly inelastic? I thought that was the definition of perfect inelasticity.

Also shouldn't the first definition use relative speed instead of relative velocity? For example, if a particle of mass m hits a wall with velocity v, it will rebound with velocity -v, so according to this definition e should be -1.