Approach to steady motion of a plate moving in a free-molecular gas under a constant external force

A thin plate accelerated or decelerated in a free-molecular gas at rest by a constant external force is considered. The force is in the direction perpendicular to the plate. In this situation, the plate velocity approaches its final constant velocity as time goes on. It is shown numerically that, under the diffuse-reflection boundary condition, the difference between the plate velocity and its final value decreases in proportion to an inverse power of time. This agrees with the previous theoretical result obtained under the assumption that the initial plate velocity is sufficiently close to the final one.