Abstract Unlike accelerated motion or curvalinear motion,a nonlinear motion state(non-inertial system) can be described by differential equations or the other algebric equations in axiom 2, the accelerated motion in axiom 3 can be considered to be described by using the equation of the linear and curvilinear process of the continuum extending to infinitely distance.Further, this linear and curvilinear process of the continuum is a quantitative continuum in essence as a unity of infinitely quantities and infinitely dimensions at infinite distance (infinity) relative to all orientations in which we exist. These indicates that an accelerated motion accumulates continuously started from a finite quantities, leaping to transit from finite to infinite quantities by an infinitely great accelerating force.