  We study a model of scalar field with a general non-minimal kinetic coupling
to itself and to the curvature. The cosmological dynamics of this model and the
issue of accelerated expansion is analyzed. Solutions giving rise to power law
expansion have been found. By constraining the potential of the model, we
obtained a variety of solutions corresponding to phenomenologically acceptable
models of dark energy, like the $\Lambda$CDM model, variable cosmological
constant model VCC, FRW with two dimensional topological defects, FRW with
phantom dark energy, showing that this model with the appropriate potential in
each case, can describe a rich variety of dynamical scenarios.
