  We show analytically and numerically that, the velocity $v_\pm$ of a particle
near the turning points $x_0$ vanishes, i. e. $v_\pm\rightarrow 0$ as
$x\rightarrow x_0$, according to the power law scaling $\left|v_\pm\right|
\propto \left|x_0-x\right|^{\beta}$, where the exponent $\beta=1/2$ is
independent of the particle mass and the force acting on it. We also show that,
the time spends it any particle at each small interval $dx$ near the turning
points diverges as $\tau\propto \left|x_0-x\right|^{\nu}$, with the exponent
$\nu=-1/2$. Behavior we find here is very similar to power law scaling that had
been found near the critical points for systems which undergo a phase
transition.
