1. The problem statement, all variables and given/known data I should know this, but it's been awhile since I've dealt w/ kinematics. As the simplest example of resisted motion of a particle, find the velocity of horizontal motion in a medium in which the retarding force is proportional to velocity. So Fr is something like -kmv, where k is a constant. I'm tempted to use v=vo+at in this manner: ma=-kmv, so a = -kv then v=vo-kvt v(1+kt)=vo v=vo/(1+kt) But my book uses integrals: mdv/dt=-kmv int(dv/v)=-k*int(dt) lnv=-kt+C , v= c1e^-kt where (c1=e^C) and applying initial conditions you get v=vo*e^-kt and this makes a lot of sense to me. So could somebody please refresh me on why I cannot solve for a and substitute into v=vo+at? I'm thinking it has to do with the constantly changing force, but I'm looking for a good explanation.