We study braneworlds in a five-dimensional bulk, where cosmological expansion is mimicked by motion through AdS5. We show that the five-dimensional graviton reduces to the four-dimensional one in the late time approximation of such braneworlds. Inserting a fixed regulator brane far from the physical brane, we investigate quantum graviton production due to the motion of the brane. We show that the massive Kaluza-Klein modes decouple completely from the massless mode and they are not generated at all in the limit where the regulator brane position goes to infinity. In the low energy limit, the massless four-dimensional graviton obeys the usual 4D equation and is therefore also not generated in a radiation-dominated universe.