We study controllable friction in a system consisting of a dark soliton in a one-dimensional Bose gas and a non-interacting Fermi gas. The fermions act as impurity atoms, not part of the original condensate, that scatter off of the soliton. We investigate semiclassical dynamics of the dark soliton, a particle-like object with negative mass, and calculate its friction coefficient. Surprisingly, the amount of friction depends on the ratio of interspecies (impurity-condensate) to intraspecies (condensate-condensate) interaction strengths. By tuning this ratio, one can access a regime where the friction coefficient vanishes. Using this friction coefficient we develop a complete kinetic theory of the soliton, including the exact probability distribution function for the soliton. We find that both the trajectory and lifetime of the soliton are altered by friction, and in the presence of friction and an external confining potential the soliton can undergo Brownian motion. These results agree qualitatively with experimental observations by Aycock, et. al (PNAS 2017) in a similar system with bosonic impurity scatterers.