This paper solves a motion planning problem from a motion safety perspective, where a variant of the classical Rapidly exploring Random Tree (RRT) approach [1] called p-safe RRT is proposed. The exploration of the search space is similar to RRT, however, the highlight of p-safe RRT is the integration of passive motion safety. The basic principle of this safety level is to guarantee that the system can brake down and stop before collision. P-safe RRT extends a tree through the state time space, where tree's nodes and primitives are checked for passive motion safety. The computed trajectory is passively safe and drives the robot from its initial state to the goal state. The developed algorithms have been tested in simulation scenarios; featuring both fixed and moving objects with unknown trajectories for a car-like robot with a limited field of view.