This is how inertia is used to dust a floor mat:
Initially, the floor mat and loose dust particles in it are at rest. But when the floor mat is hit with a stick, it is suddenly put into motion, but the dust particles in it will try to remain in the state of rest because of inertia of rest, hence the dust comes out of the floor mat.
Inertia is a property of a body due to which it resists a change in its state of rest or of uniform motion When we give a suddent jerk to a wet cloth, the force of the jerk displaces the cloth. However, water continues in its state of rest , and in the absence of the cloth falls off to the floor. This is how inertia is used to remove water drops from a wet cloth.