(b) Link AC is used to drive the peg at B along a grooved circular guide as shown. At the instant and configuration shown where $\theta = \tan^{-1}(5/12)$, b = 240 mm and e = 100 mm, peg B moves with a velocity v = 1.5 m/s in the direction as shown and is increasing at 19.5 m/s².
(i) Determine at this instant the velocity and acceleration of peg B in rectangular and normal-tangential coordinates.
(ii) Determine at this same instant the corresponding values of $\dot{r}$, $\dot{\theta}$, $\ddot{r}$, and $\ddot{\theta}$.
[CO2/PO1/C4](13 marks)
(c) The study of kinematics of the motion of a particle requires the relations between position, velocity, acceleration and time. Evaluate the present of $\ddot{\theta}$ in the transverse component of the acceleration i.e. $a_{\theta} = \dot{r}\dot{\theta} + 2\dot{r}\dot{\theta}$.
[CO3/PO2/C6](2 marks)
