To obtain the high-speed metal particles in simulating the impact of meteoroids and fragments of space debris on the spacecraft protective screens, shock-wave acceleration of thin metal plates is used at their collision with the impact element accelerated by a light-gas ballistic installation. Such an element is provided at the front end with an insert of layers with acoustic stiffness decreasing outwards. The effect of increasing speed of a plate accelerated by the plate impact is considered, when an intermediate system of plates with monotonically decreasing acoustic impedance is installed between it and the impact element, which values are between the impact element and the accelerated plate impedances. Based on numerical simulation in the framework of a plane one-dimensional problem of continuum mechanics, the shock-wave acceleration of an aluminum plate was studied in its direct collision with a tantalum impact element, as well as in the presence of one intermediate plate of copper or two intermediate plates of copper and titanium between them. An increase in the coefficient of accelerated plate raising speed relative to the impact element speed was registered with an increase in the number of intermediate plates. Using acoustic approximation, an analytical solution to the problem of plate acceleration in the presence of a system of the infinite number of infinitely thin plates with the continuously decreasing acoustic impedance between it and the impact element was obtained.