Hi physics120!
Quote by physics120
Momentum conservation requires (m1 + m2) * vf = m1v1 +m2v2. Because v1>v2, it must be that (m1 +m2) * vf = m1v1 + m2v2 > m1v2 +m2v2 = (m1 + m2) * v2. Thus vf > v2. Similarly, v2 < v1 so (m1 + m2) * vf = m1v1 + m2v2 < m1v1 + m2v1 = (m1 + m2) * v1. Thus vf < v1. The collision causes m1 to slow down and m2 to speed up.

hmm … works even if v1 < v2 …
personally, I'd write it vf = pv1 + (1p)v2,
where p = m1/(m1 + m2),
and then obviously vf lies between v1 and v2.
but anyway, what part of the proof in the book is worrying you?