Another simplification I've made:

In the following ODE:

dV / Q(K / Rw * V) = (K / Rw / m) * dt,

you may object that the left-hand side blows up at V=0. Indeed, that's where the clutch or torque converter comes in, they make sure that at V=0, the engine still has idle rpm and therefore can transmit positive torque.

If you don't like my simplification, then consider a rolling acceleration 5-60 and integrate the left-hand side from V=5 and on. This way you don't need to model clutch behavior.