Based on the Enss-Weder time-dependent method, we study one of multidimensional inverse scattering problems for quantum systems in an external electric field asymptotically zero in time as $E_0(1+|t|)^{-\mu}$ with $0<\mu<1$, where $E_0$ is a non-zero constant electric field. We show that when the space dimension is greater than or equal to two, the high velocity limit of the scattering operator determines uniquely the short-range potential like $|x|^{-\gamma}$ with $\gamma>1/(2-\mu)$. Moreover, we prove that the high velocity limit of any one of the Dollard-type modified scattering operators determines uniquely the total potential.