Chapter 12 - Kinematics of a Particle - Section 12.8 - Curvilinear Motion: Cylindrical Components - Problems - Page 80: 162

$v_r=ae^{at}$ $v_\theta=e^{at}$ $a_r=e^{at}(a^2-1)$ $a_\theta=2ae^{at}$

$r=e^{at}$ $\dot{r}=ae^{at}$ $\ddot{r}=a^2e^{at}$ $\theta=t$ $\dot{\theta}=1$ $\ddot{\theta}=0$ $v_r=\dot{r}=ae^{at}$ $v_\theta=r\dot{\theta}=e^{at}$ $a_r=\ddot{r}-r\dot{\theta}^2=a^2e^{at}-e^{at}(1)^2=e^{at}(a^2-1)$ $a_\theta=r\ddot{\theta}+2\dot{r}\dot{\theta}=e^{at}(0)+2(ae^{at})(1)=2ae^{at}$