The current paper presents a simple mathematical model for replication of the transient acceleration motion of displacement hulls in calm water under the action of a propulsion system. Different empirical methods are coupled, and an operational speed problem is solved in the time domain. The resistance of the ship is calculated by using the Holtrop method. The values of thrust force, torque and propeller efficiency are computed by using B-Series empirical equations. The acceleration motion of the vessel, which is triggered as the engine starts to work, is simulated by solving a set of first-order differential equations, which are discretised in the time domain. It is shown that different propellers can lead to different transient and steady behaviours of the vessel. Finally, using a genetic algorithm library, it is demonstrated that the method can be helpful and be easily linked to the design process. Moreover, an optimisation study is performed, showing that, the developed method provides an efficient propeller, under the action of which ship reaches the maximum possible speed in the earliest possible time with the highest efficiency for the propeller. The current method can be useful in the mathematical reproduction of the ship-propeller-engine, which needed to be modified in future.