The distance resolution $\Delta d$ is inversly proportional to the bandwidth and can be determined by \begin{equation} \Delta d=\frac{c_0}{2N\Delta f}. \end{equation} The distance to an object is only umambiguous as long as $\tau \Delta f<1$. This translates to a maximum unambigous distance of \begin{equation} \label{eqn:DistanceUnambiguous} d_\mathrm{unamb}=\frac{1}{2}\tau_\mathrm{unamb}c_0=\frac{c_0}{2\Delta f}. \end{equation} This means that an object at distance $d_\mathrm{unamb}+d$ will appear as if it was at a distance $d$. The maximum distance is therefore limited by the subcarrier spacing $\Delta f$ .
The velocity resolution $\Delta v_\mathrm{rel}$ is inversely propotional to the frame duration and can be determined in similar fashion, \begin{equation} \Delta v_\mathrm{rel}=\frac{c_0}{2MT_\mathrm{O}f_\mathrm{C}}. \end{equation} The velocity is unambiguous for $|f_\mathrm{D}T_\mathrm{O}|<\frac{1}{2}$. The maximum absolute relative velocity is therefore \begin{equation} \label{eqn:VelocityUnambiguous} v_\mathrm{rel, unamb}=\frac{f_\mathrm{D, unamb}c_0}{2f_\mathrm{C}}=\frac{c_0}{2f_\mathrm{C}T_\mathrm{O}}. \end{equation} This means that the relative velocity can only be correctly identified as long as the object's velocity $|v|<v_\mathrm{rel, unamb}$ .