Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_199

2/199 At the instant depicted, assume that the particle $P$, which moves on a curved path, is $80\text{ m}$ from the pole $O$ and has the velocity $v$ and acceleration $a$ as indicated. Determine the instantaneous values of $\dot{r}$, $\ddot{r}$, $\dot{\theta}$, $\ddot{\theta}$, the $n$- and $t$-components of acceleration, and the radius of curvature $\rho$. From the diagram: $r = 80\text{ m}$ (distance from $O$ to $P$) $v = 30\text{ m/s}$ at an angle of $30^\circ$ relative to the radial direction $r$. $a = 8\text{ m/s}^2$ at an angle of $30^\circ$ relative to the velocity vector $v$. The $r$ vector makes an angle of $60^\circ$ with the horizontal.