<p>The subject of this study is the dynamics of variable-mass systems in which the mass varies as a function of time or position. The research is particularly focused on determining the system velocity, which is usually obtained by solving the equations of motion which are very complex for variable-mass systems. The aim of this paper is to develop a new method that is simpler and more suitable for determining velocity. By applying the analytical theory of impact and assuming that the change of mass is due to a perfectly plastic impact of particles, the Meshchersky–Lagrange equation is derived, which includes the impulse of the reactive force. The impulse of the reactive force, resulting from the mass variation, is equal to the product of the mass of the particle that is attached to or detached from the system and its absolute velocity. The equation represents the first integral of the Lagrange equation for variable-mass systems in which the kinetic energy has a quadratic form in the velocity, and the coefficient depends either on time or on position. Under these constraints, the newly obtained formula has been applied to calculate velocity in the Tsiolkovsky rocket problem, in surface coating systems, and in mass collection facilities.</p>