  A specific class of explicitly time-dependent potentials is studied by means
of path integrals. For this purpose a general formalism to treat explicitly
time-dependent space-time transformations in path integrals is sketched. An
explicit time-dependent model under consideration is of the form
$V(q,t)=V[q/\zeta(t)]/\zeta^2(t)$, where $V$ is a usual potential, and
$\zeta(t)=(at^2+2bt+c)^{1/2}$. A recent result of Dodonov et al.\ for
calculating corresponding propagators is incorporated into the path integral
formalism by performing a space-time transformation. Some examples illustrate
the formalism.
