Consider the mechanism shown below. Collar $D$ is free to slide along bar $BC$. Given: $\Omega_{AB} = 0, \dot \Omega_{AB} = 0, \Omega_{BC} = 1$ $rad/s$ $\hat{k}$ and $(v_{D/B})_{x'y'z'} = 1/2$ $m/s$ $\hat{i}$, what are $\dot \Omega_{BC}$ and $(a_{D/B})_{x'y'z'}$ such that the absolute acceleration of the centre of collar $D$ is zero?

A. $\dot \Omega_{BC} = 2$ $rad/s^2$ $\hat{k}$ and $(a_{D/B})_{x'y'z'} = 1/2$ $m/s^2$ $\hat{i}$
B. $\dot \Omega_{BC} = 1$ $rad/s^2$ $\hat{k}$ and $(a_{D/B})_{x'y'z'} = 2$ $m/s^2$ $\hat{i}$
C. $\dot \Omega_{BC} = -2$ $rad/s^2$ $\hat{k}$ and $(a_{D/B})_{x'y'z'} = 1/2$ $m/s^2$ $\hat{i}$
D. $\dot \Omega_{BC} = 1$ $rad/s^2$ $\hat{k}$ and $(a_{D/B})_{xyz} = -2$ $m/s^2$ $\hat{i}$
E. $\dot \Omega_{BC} = -1$ $rad/s^2$ $\hat{k}$ and $(a_{D/B})_{x'y'z'} = -2$ $m/s^2$ $\hat{i}$
F. $\dot \Omega_{BC} = 0$ $rad/s^2$ $\hat{k}$ and $(a_{D/B})_{x'y'z'} = 0$ $m/s^2$ $\hat{i}$
G. None of the above