To remove the dus

There is same principle in this case which is about inertia which is that the sand particles are at rest along with the carpet and are resting on carpet , as soon as we hit the carpet with a stick we apply a force very fast and within a short interval of time which does not affect the sand particles because they are at inertia of rest but the force acts on the carpet which moves the carpet and the dust particles fall down because they do not move with the carpet.

As we apply force on carpet it is no longer in inertia, so the only thing possessing inertia in this question is dust particles.