  We study the biased diffusion of particles moving in one direction under the
action of a constant force in the presence of a piecewise linear random
potential. Using the overdamped equation of motion, we represent the first and
second moments of the particle position as inverse Laplace transforms. By
applying to these transforms the ordinary and the modified Tauberian theorem,
we determine the short- and long-time behavior of the mean-square displacement
of particles. Our results show that while at short times the biased diffusion
is always ballistic, at long times it can be either normal or anomalous. We
formulate the conditions for normal and anomalous behavior and derive the laws
of biased diffusion in both these cases.
