  We use the extended relaxation time approximation for the collision kernel,
which incorporates a particle-energy dependent relaxation time, to derive
second-order viscous hydrodynamics from the Boltzmann equation for a system of
massless particles. The resulting transport coefficients are found to be
sensitive to the energy dependence of the relaxation time and have significant
influence on the fluid's evolution. Using the derived hydrodynamic equations,
we study the evolution of a fluid undergoing (0+1)-dimensional expansion with
Bjorken symmetry and investigate the fixed point structure inherent in the
equations. Further, by employing a power law parametrization to describe the
energy dependence of the relaxation time, we successfully reproduce the stable
free-streaming fixed point for a specific power of the energy dependence. The
impact of the energy-dependent relaxation time on the processes of
isotropization and thermalization of an expanding plasma is discussed.
