# Question about dynamic window approach?

I have a my mobile robot and plan to use the dynamic window approach to collision avoidance. I have read the paper ,but have one inequality i can't derive it. could you tell me? thanks!

This falls out of the basic equations of motion for a body under constant acceleration. The simplest thing is to start with this equation: $$v^2 = v_o^2 + 2ad$$ Where we are starting at some velocity $v$, and decelerating at $a$ (or $\dot{v}$ in your equation) to a stop. (So $v_o$ = 0). The distance traveled, $d$, must be less than the distance to the obstacle, $dist(v,w)$.