Since the finite time stabilization is very important in many actual applications, finite time control systems have been studied a lot. Terminal sliding mode control system is a robust control scheme which guarantees that the error gets to zero in a finite time. The terminal sliding mode controller uses terminal sliding surface utilizes a power function whose exponent is a rational number 0 to 1. This exponent affects the convergence time. Thus, in this paper, for DC motor systems, we derived a condition on the exponent to guarantee the minimum convergence time.