r = D \cos(\theta)
A camera on the left edge of a circular track of radius D = 4 m tracks a particle as it travels around the circle. The polar equation of the path is given above.
At the moment shown, the camera angle is $\theta = 30^\circ$, and the camera is rotating at $\dot{\theta} = 0.5 \text{ rad/s}$, which is accelerating at a rate $\ddot{\theta} = -0.1 \text{ rad/}s^2$. What is the velocity, acceleration, and rate of change of speed of the particle at that instant?
v = ____ m/s
a = ____ m/s$^2$
$\dot{v}$ = ____ m/s$^2$