In this paper, we consider a particle moves on a space curve in the
Euclidean 3-space and resolve its acceleration and jerk vectors
according to quasi-frame. In this resolution, by appyling Siacci's
theorem, we state the acceleration vector as the sum of its tangential
and radial components, and obtain the jerk vector along the tangential
direction and radial directions in osculating and rectifying planes. On
the basis of the jerk vector formula , we give the maximum admissible
speed on a space curve at all trajectory points. Furthermore, we present
illustrative examples to explain how our results work.