A known mathematical model of a cart coupled to a DC motor with a small inductive term is studied here. It is a system of differential equations in a dimensionless form with a small parameter standing before one derivative i. e. a singularly perturbed system. The degenerate system, where the small parameter is equal to zero, corresponds to eliminating the inductive term from the electrical equation. The mathematical justification, using Tikhonov’s theorem, of considering the degenerate model instead the full one is given. In general case, the fast variable from a solution of an initial value problem for the full model is not close to the corresponding solution of the degenerate model near the starting point. The zero-order uniform asymptotic solution for the considered model is constructed with the help of boundary functions method by A. B. Vasil’eva. The given in this paper graphs illustrate Tikhonov’s theorem and a uniform proximity of the constructed asymptotic approximation to the exact solution in a neighborhood of the starting point.