We study one of multidimensional inverse scattering problems for quantum systems in time-dependent electric fields $E(t)$, which is represented as $E_0(1+|t|)^{-\mu}$ with $0\le\mu<1$, based on the Enss-Weder time-dependent method. 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 part like $|x|^{-\gamma}$ with $\gamma>1/(2-\mu)$ of the potential belonging to the class rather wider than the one given by Adachi-Kamada-Kazuno-Toratani. Our method can also improve previous results in the case where $E(t)$ is periodic in $t$ with non-zero mean $E_0$.