Sunday night physics problems :( Alright, so I'm supposed to find the displacement equation for a particle fired vertically under a constant gravitational field, where the resisting force is proportional to the instantaneous velocity of the particle. Here's where I'm at: Fup = ma; Fdown = -mg - kmv; Fnet = (ma) + (-mg - kmv) // Where k is a constant ma = (ma) + (-mg - kmv) // Force = Fup + Fdown dv/dt = -g - kv // m's cancel, differentiate wrt v dv * 1/(-g -kv) = -dt // Integrating... 1/k ln(kv+ g) = -t + c0 // Where c0 represents initial velocity ln(kv + g) = -tk + kc0 kv + g = e^(-tk + kc0) v = [ e^(-tk + kc0) - g ] / k Integrate wrt t, to obtain position ( v(t) ) v(t) = -g/k + -------> ???? <---------- The answer is supposed to simplify to: v(t) = [-g/k] + [ (kc0 + g) / k] * e^(-kt) I have no idea how. I have no idea where the g in the second term came from in the first place. Thanks ahead of time!