I spent a great amount of time on this part you are mentioning. The book does not provide a great description on this statement.
"Where -kmv represents a positive upward force since we take z and v = z(dot) to be positive upward, and the motion is downward-that is, v<0, so that -kmv > 0."
I...
Example problem from a Classical Mechanics book.
Find the displacement and velocity of a particle undergoing vertical motion in a medium having a retarding force proportional to the velocity.
F = m(dv/dt) = -mg-kmv
dv/(kv + g) = -dt
(1/k)ln(kv + g) = -t + c
kv + g = e^(-kt+kc)
v =...