= Solution
The perpendicular <unit vectors> represented by $e^{i\theta}$ and $ie^{i\theta}$ point radially outwards and transversely in the increasing-angle direction. Reading off their real coefficients in part (b) gives the signed components
$$
\boxed{v_r=\dot r,\qquad v_\theta=r\dot\theta,\qquad
a_r=\ddot r-r\dot\theta^2,\qquad
a_\theta=2\dot r\dot\theta+r\ddot\theta.}
$$
These are <velocity in polar coordinates> and <acceleration in polar coordinates>. In particular $r\dot\theta$ is a transverse <speed> component; $\dot\theta$ alone is an <angular velocity>. The moving <basis>, rather than any extra force assumption, accounts for the additional <acceleration> terms. At the origin the polar directions themselves are undefined, although the Cartesian <velocity> and <acceleration> can remain well defined.
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