We consider the effect of accelerated magnetopause motions arising from the arrival of a modified-pressure region of the solar wind with a sharp forefront upon the growth rate of the velocity shear layer instability. The range of values of relative pressure variation on the front was taken to lie within 1.25--2, and the front thickness ranged from 200 km to 1RE (6400 km). At different phases of motion of the boundary, the instability growth rate can change in either direction as a consequence of the Rayleigh--Taylor effect, in accordance with a change of sign of acceleration g of the boundary. The typical time during which of the boundary remains inside the new equilibrium position (≤1 min) is sufficient for the instability to reach the nonlinear regime. It is possible that plasma flutes on the boundary penetrate the magnetosphere. Generation of disturbances can be modulated by boundary oscillations inside the new equilibrium position. We discuss the interplanetary magnetic field influence upon the growth rate of the MHD instability under consideration. An analysis is made of a number of daytime geophysical conditions which cannot be understood when interpreted in terms of the instability on a stationary boundary. ¿ American Geophysical Union 1993