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We study the motion of a heavy tracer particle weakly coupled to a denseinteracting Bose gas exhibiting Bose-Einstein condensation. In the so-calledmean-field limit, the dynamics of this system approaches one determined bynonlinear Hamiltonian evolution equations. We derive the effective dynamics ofthe tracer particle, which is described by a non-linear integro-differentialequation with memory, and prove that if the initial speed of the tracerparticle is below the speed of sound in the Bose gas the motion of the particleapproaches an inertial motion at constant velocity at large times.

Ballistic Motion of a Tracer Particle Coupled to a Bose gas