  We study the one-dimensional boost-invariant Boltzmann equation in the
relaxation-time approximation using special moments of the distribution
function for a system with a finite particle mass. The infinite hierarchy of
moments can be truncated by keeping only the three lowest moments that
correspond to the three independent components of the energy-momentum tensor.
We show that such a three-moment truncation reproduces accurately the exact
solution of the kinetic equation after a simple renormalization that takes into
account the effects of the neglected higher moments. We derive second-order
Israel-Stewart hydrodynamic equations from the three-moment equations, and show
that, for most physically relevant initial conditions, these equations yield
results comparable to those of the three-moment truncation, albeit less
accurate. We attribute this feature to the fact that the structure of
Israel-Stewart equations is similar to that of the three-moment truncation. In
particular, the presence of the relaxation term in the Israel-Stewart
equations, yields an early-time regime that mimics approximately the
collisionless regime. A detailed comparison of the three-moment truncation with
second-order non-conformal hydrodynamics reveals ambiguities in the definition
of second-order transport coefficients. These ambiguities affect the ability of
Israel-Stewart hydrodynamics to reproduce results of kinetic theory.
