  We unravel the nonequilibrium correlated quantum quench dynamics of an
impurity traveling through a harmonically confined Bose-Einstein condensate in
one-dimension. For weak repulsive interspecies interactions the impurity
oscillates within the bosonic gas. At strong repulsions and depending on its
prequench position the impurity moves towards an edge of the bosonic medium and
subsequently equilibrates. This equilibration being present independently of
the initial velocity, the position and the mass of the impurity is inherently
related to the generation of entanglement in the many-body system. Focusing on
attractive interactions the impurity performs a damped oscillatory motion
within the bosonic bath, a behavior that becomes more evident for stronger
attractions. To elucidate our understanding of the dynamics an effective
potential picture is constructed. The effective mass of the emergent
quasiparticle is measured and found to be generically larger than the bare one,
especially for strong attractions. In all cases, a transfer of energy from the
impurity to the bosonic medium takes place. Finally, by averaging over a sample
of simulated in-situ single-shot images we expose how the single-particle
density distributions and the two-body interspecies correlations can be probed.
