  We employ equation of motion techniques to study the non-equilibrium dynamics
in a lattice model of weakly interacting spinless fermions. Our model provides
a simple setting for analyzing the effects of weak integrability breaking
perturbations on the time evolution after a quantum quench. We establish the
accuracy of the method by comparing results at short and intermediate times to
time-dependent density matrix renormalization group computations. For
sufficiently weak integrability-breaking interactions we always observe
prethermalization plateaux, where local observables relax to non-thermal values
at intermediate time scales. At later times a crossover towards thermal
behaviour sets in. We determine the associated time scale, which depends on the
initial state, the band structure of the non-interacting theory, and the
strength of the integrability breaking perturbation. Our method allows us to
analyze in some detail the spreading of correlations and in particular the
structure of the associated light cones in our model. We find that the interior
and exterior of the light cone are separated by an intermediate region, the
temporal width of which appears to scale with a universal power-law $t^{1/3}$.
