The motion of a particle on the surface of a right circular cone is defined by the relations R = ht tan$\beta$, $\theta$=2$\pi$t, and z = ht, where $\beta$ is the apex angle of the cone and h is the distance the particle rises in one passage around the cone. Determine the magnitudes of the velocity and acceleration at any time t.
I don't know what I should differentiate between getting the equation enter image description here
$R=ht\tan\beta$→$\dot{R}=h\tan\beta$→$\ddot{R}=0$ , $\theta=2\pi t$ → $\dot{\theta}=2\pi$ → $\ddot{\theta}=0$ , $Z=ht$ → $\dot{Z}=h$ → $\ddot{Z}=0$
$v_R=h\tan\beta$ , $v_{\theta}=2\pi ht\tan\beta$ , $v_Z=h$ → $a_R=-4\pi^2ht\tan\beta$ , $a_{\theta}=4\pi h \tan\beta$ , $a_Z=0$