[en] We experimentally investigate the two- and three-body breakup dynamics of N₂O${}^{q+}$ ($q=2,3$) under the impact of fast (5 keV) electrons using a coincidence momentum spectroscopy technique. The kinetic energy release (KER) distributions have been derived from the measured momenta for various breakup channels. The present values are found to be quite different from a previously reported high energy electron impact study. From the measured momentum vectors, the geometry of the precursor molecular ion prior to the fragmentation has been reconstructed. The three-body decay dynamics of N₂O³⁺ has been studied using Dalitz plots and Newton diagrams with a view of concerted and sequential decay mechanisms. It is found that the sequential process is present along with the concerted process for the N₂O³⁺ $\to <!--\; ???\; -->$ N⁺ + NO²⁺ $\to <!--\; ???\; -->$ N⁺ + N⁺ + O⁺ channel. (paper)