In this paper, we investigate the solvation dynamics of the weakly polar organic solvent tetrahydrofuran (THF) via classical molecular dynamics simulation. We find that the relaxation dynamics of all of the rotational and translational degrees of freedom of neat THF occur on similar time scales and have similar power spectra, making it impossible to use spectral density analysis to discern which specific molecular motions are involved in solvation. Instead, we probe the molecular origins of solvation dynamics using a nonequilibrium projection formalism that we originally outlined in M. J. Bedard-Hearn et al., J. Phys. Chem. A 2003, 107 (24), 4773. Here, we expand this formalism and use it to study the nonequilibrium solvation dynamics for a model reaction in THF in which a charge is removed from an anionic Lennard-Jones (U) solute, leaving behind a smaller neutral atom. The solute parameters are chosen to model the photodetachment of an electron from a sodium anion, Na- --> Na-0, to compare to the results of ultrafast spectroscopic experiments of this reaction being performed in our lab. We are able to explain the hidden breakdown of linear response for this system that we uncovered in our previous work in terms of the dynamical properties of the neat liquid and the structural properties of the solutions. In particular, our nonequilibrium projection analysis shows that four distinct solvation mechanisms are operative: (1) a rapid relaxation (t less than or equal to 700 fs) caused by longitudinal translational motions that dramatically change the local solvation structure; (2) a slower relaxation (t > 700 fs) caused by diffusive longitudinal translational motions that completes the transformation of the long-range solute-solvent packing; (3) an early-time relaxation (t < 500 fs) caused by solvent rotational motions that destabilizes the (unoccupied) anion ground state via Coulomb interactions; (4) a longer time process (t greater than or equal to 500 fs) caused by solvent rotational motions that increases the solvation energy gap. This last process results from the LJ interaction component of the solvent rotational motions, as the nonequilibrium dynamics bring smaller THF-oxygen sites closer to the excited solute in place of larger THF-methylene sites. Overall, the simulations indicate that nonequilibrium solvation dynamics involves cooperative motions of both the solute and solvent and consists of multiple competing relaxation processes that can affect the solvation energy gap in opposite directions.