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We follow the dynamical evolution of young star-forming regions with a widerange of initial conditions and examine how the radial velocity dispersion,$\sigma$, evolves over time. We compare this velocity dispersion to thetheoretically expected value for the velocity dispersion if a region were invirial equilibrium, $\sigma_{\rm vir}$ and thus assess the virial state($\sigma / \sigma_{\rm vir}$) of these systems. We find that in regions thatare initially subvirial, or in global virial equilibrium but subvirial on localscales, the system relaxes to virial equilibrium within several million years,or roughly 25 - 50 crossing times, according to the measured virial ratio.However, the measured velocity dispersion, $\sigma$, appears to be a baddiagnostic of the current virial state of these systems as it suggests thatthey become supervirial when compared to the velocity dispersion estimated fromthe virial mass, $\sigma_{\rm vir}$. We suggest that this discrepancy is causedby the fact that the regions are never fully relaxed, and that the earlynon-equilibrium evolution is imprinted in the one-dimensional velocitydispersion at these early epochs. If measured early enough ($<$2 Myr in oursimulations, or $\sim$20 crossing times), the velocity dispersion can be usedto determine whether a region was highly supervirial at birth without the riskof degeneracy. We show that combining $\sigma$, or the ratio of $\sigma$ to theinterquartile range (IQR) dispersion, with measures of spatial structure,places stronger constraints on the dynamical history of a region than using thevelocity dispersion in isolation.

Dynamical evolution of star forming regions - II. Basic kinematics