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Synthetic aperture radars (SAR) installed on aircrafts or satellites are able to obtain images of a scene with high spatial resolution. SAR data processing is a kind of optimal filtering of signals from static point scatterers. Signals received from moving targets are processed with the mismatched filter. It means that moving targets appear to be defocused and displaced from their true positions in radar images; therefore it is difficult to obtain information about moving targets from an ordinary SAR image. Nevertheless, the problem of detection of moving targets by SAR is important for many practical applications. One of the methods applied to solve the problem by using a common single-antenna SAR is based on multi-look processing, which consists in forming several image looks of the same scene patch from the data collected on different time intervals. The idea is that the static targets in the SAR image looks preserve their positions while the moving targets appear to be shifted, which allows distinguishing the moving targets from the static ones. Moreover, some motion parameters can be estimated via the target displacements. In this paper, formulas that describe the displacement of a moving target in SAR images are derived on the basis of the common equations of the multi-look SAR processing in time domain under the assumption that the target velocity vector is constant. It is found that in the framework of such approach one can determine the range to the target, the module and the radial component of the relative velocity vector of the target. In order to find true position of the target and its own velocity vector some additional information is required, for example, the target trajectory. Otherwise, the ambiguity between the target position and velocity is preserved. The obtained theoretical results are illustrated with computer simulations.