  Local stresses in a tissue, a collective property, regulate cell division and
apoptosis. In turn, cell growth and division induce active stresses in the
tissue. As a consequence, there is a feedback between cell growth and local
stresses. However, how the cell dynamics depend on local stress-dependent cell
division and the feedback strength is not fully understood. Here, we probe the
consequences of stress-mediated growth and cell division on cell dynamics using
agent-based simulations of a two-dimensional growing tissue. We discover a rich
dynamical behavior of individual cells, ranging from jamming (mean square
displacement, $\Delta (t) \sim t^{\alpha}$ with $\alpha$ less than unity), to
hyperdiffusion ($\alpha > 2$) depending on cell division rate and the strength
of the mechanical feedback. Strikingly, $\Delta (t)$ is determined by the
tissue growth law, which quantifies cell proliferation (number of cells $N(t)$
as a function of time). The growth law ($N(t) \sim t^{\lambda}$ at long times)
is regulated by the critical pressure that controls the strength of the
mechanical feedback and the ratio between cell division-apoptosis rates. We
show that $\lambda \sim \alpha$, which implies that higher growth rate leads to
a greater degree of cell migration. The variations in cell motility are linked
to the emergence of highly persistent forces extending over several cell cycle
times. Our predictions are testable using cell-tracking imaging techniques.
