To obtain high-velocity metal particles, when modeling the impact of meteoroids and debris fragments on the protective screens of spacecraft, shock-wave acceleration of thin metal plates is used when they collide with an impact element accelerated by a light-gas ballistic installation and having an insert of layers with decreasing acoustic rigidity on the front end. The effect of increasing the velocity of the plate accelerated by impact is considered when placing between it and the impactor an intermediate system of plates with monotonically decreasing acoustic impedance, the values of which are enclosed between the impedances of the impactor and the accelerated plate. On the basis of numerical modeling in the framework of a plane one-dimensional problem of continuum mechanics, the shock-wave acceleration of an aluminum plate is investigated when it directly collides with a tantalum impactor, as well as when there is one intermediate plate of copper or two intermediate plates of copper and titanium between them. An increase in the coefficient of increase in the velocity of the accelerated plate relative to the velocity of the impactor is recorded when increasing in the number of intermediate plates. Using the acoustic approximation, an analytical solution to the problem of plate acceleration is obtained in the presence between it and the impactor of a system of an infinite number of infinitely thin plates with continuously decreasing acoustic impedance.