  We revisit the problem of the critical velocity of a clean one-dimensional
superconductor. {\changed At the level of mean-field theory}, we find that the
zero-temperature value of the critical velocity--the uniform velocity of the
superfluid condensate at which the superconducting state becomes unstable--is a
factor of $\sqrt{2}$ smaller than the Landau critical velocity. This is in
contrast to a prior finding, which held that the critical velocity is equal to
the Landau critical velocity. The smaller value of the critical velocity, which
our analysis yields, is the result of a pre-emptive
Clogston-Chandrasekhar--like discontinuous phase transition, and is an analog
of the threshold value of the uniform exchange-field of a superconductor,
previously investigated by Sarma and by Maki and Tsuneto. We also consider the
impact of nonzero temperature, study critical currents, and examine
metastability and its limits in the temperature versus flow-velocity phase
diagram. In addition, we comment on the effects of electron scattering by
impurities.
