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In this paper, we use the quantum variational calculus related to Hahn'sdiscrete time derivative construct the deformed version for the classicalmechanics related to the Hahn's calculus. We deal with the deformed dynamicssuch as the motion with constant velocity and the motion with constantacceleration. Moreover, we extend our work to the motion of a body in aresisting medium by using the new identity for an infinite ($q,w$)-series,where the retarding force is assumed to be proportional to the deformed averagevelocity.

Study on the mechanical system related to Hahn's discrete time derivative