  We use Newtonian and overdamped Langevin dynamics to study long flexible
polymers dragged by an external force at a constant velocity $v$. The work $W$
by that force depends on the initial state of the polymer and the details of
the process. Jarzynski equality can be used to relate the non-equilibrium work
distribution $P(W)$ obtained from repeated experiments to equilibrium free
energy difference $\Delta F$ between the initial and final states. We use the
power law dependence of the geometrical and dynamical characteristics of the
polymer on the number of monomers $N$ to suggest the existence of a critical
velocity $v_c(N)$, such that for $v<v_c$ the reconstruction of $\Delta F$ is an
easy task, while for $v$ significantly exceeding $v_c$ it becomes practically
impossible. We demonstrate the existence of such $v_c$ analytically for ideal
polymer in free space and numerically for a polymer being dragged away from a
repulsive wall. Our results suggest that the distribution of the dissipated
work $W_{\rm d}=W-\Delta F$ in properly scaled variables approaches a limiting
shape for large $N$.
