Understanding the flux-line dynamics in layered superconductors is of utmost importance for many superconductor applications, yet extracting from measurements the relevant parameters remains a major challenge. Here we report on measurements and theoretical model calculations of voltage-current $(V$-$I)$ characteristics of a superconducting Ba${}_{0.72}{\mathrm{K}}_{0.28}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$ single crystal slightly below its transition temperature in perpendicular magnetic fields between 0.01 and 7 T. We propose a model that describes the flux-line dynamics above, as well as below, the depinning current. The model fits the experimental $V$-$I$ characteristics remarkably well and is used to extract from the data the field dependence of (a) the depinning current, (b) the pinning potential barrier height, (c) the dissipative resistance, and (d) the product between flux-line bundle volume and bundle hopping distance. The model also leads to an estimate of the average distance between pins.