[math-fun] Help with linear motion problem

This is a linear motion problem (actually a work problem). At time 0, a particle is at distance 0 and known velocity v (d(0) = 0, v(0) = v). At known time t, the particle comes to a stop at known distance d (d(t) = d, v(t) = 0). Velocity decreases over the entire motion (a(x) <= 0 for 0 <= x <= t). The particle never reverse direction (v(x) >= 0 for 0 <= x <= t). I don't think this is soluble with constant acceleration (a(t) = c), perhaps with acceleration linear in time?