  We prove an adiabatic theorem for the Landau-Pekar equations. This allows us
to derive new results on the accuracy of their use as effective equations for
the time evolution generated by the Fr\"ohlich Hamiltonian with large coupling
constant $\alpha$. In particular, we show that the time evolution of Pekar
product states with coherent phonon field and the electron being trapped by the
phonons is well approximated by the Landau-Pekar equations until times short
compared to $\alpha^2$.
