The under keel clearance (UKC) is considered as one of the most important factor which governs the navigation safety in restricted waterways. However, the notion of safe under keel clearance is directly related to ship sinkage. The recent researches to evaluate ship sinkage show that it is related to vessel potential energy. The curve of vessel displacement in heave motion as function of potential energy shows that a ship has three equilibrium positions; stable equilibrium position represents steady squat and unstable equilibrium position which can be considered as a virtual bottom for a ship, the third stable equilibrium position does not have any physical signification, since it lies below the bottom. The principal goal of this paper is to develop a mathematical model for vessel motion during acceleration phase by considering several assumptions. Then, analyze the conversion of kinetic energy to potential energy at the unstable equilibrium position during acceleration phase. By taking into account the period during which the vessel accelerates as well as the vessel speed at the end of the acceleration phase. The results show that ship stability could be affected by the oscillations generated at the end of this phase.