  We have used a combination of linear response time-domain THz spectroscopy
(TDTS) and high-field non-linear THz spectroscopy to separately probe the
electronic momentum and energy relaxation rates respectively of the Dirac
semimetal Cd$_3$As$_2$. We find, consistent with prior measurements, that
Cd$_3$As$_2$ has an enormous nonlinearities in the THz frequency range. We
extract the momentum relaxation rate of Cd$_3$As$_2$ using Drude fits to the
optical conductivity. We also conduct THz range 2D coherent spectroscopy. The
dominant response is a pump-probe signal, which allow us to separately extract
the energy relaxation rate. We find that the rate of energy relaxation
decreases down to the lowest measured temperatures. We connect this to
Cd$_3$As$_2$ anomalous lattice dynamics, evidence for which is found in its low
thermal conductivity and soft phonons in Raman scattering. The lack of a peak
in the energy relaxation rate as a function of T can be connected to the linear
in T dependence of the current relaxation e.g. the phonon scattering is elastic
down to the lowest measured temperatures approximately 120 K.
