Problem with constrains solving ordinary diff. equations

I want to solve the following ord. diff. eq.. This is very simple example for a moving acceöeratet body. I want to eliminate the constants C[1] and C[2] with constrains like the speed at the time of 0=v0 and the way at the time of 0=0

(∂_t)s[0]==v0,s[0]==0

Loesung$s$von$t=DSolve[{m (∂_(t,t))s[t]-m g μ==0,(∂_t)s[0]==v0,s[0]==0},s[t],t]

DSolve gives the warning:

DSolve::"nvld": "The description of the equations appears to be ambiguous or invalid."

By hand it is easy to see that C[2] must be v0:

s$von$t=(s[t]/.Loesung$s$von$t)[[1]]

(∂_t) s$von$t==v0/.t->0

Why does not Mathematica does this by itself?