In recent years many powerful techniques and algorithms have been developed to detect moving targets and estimate their motion parameters from single- or multi-channel SAR data. In case of single- and two-channel systems, most of the developed algorithms rely on analysis of the Doppler history. It is known that the Doppler shift relates mainly to ground moving target’s across-track velocity and the Doppler slope to moving target’s along-track velocity and across-track acceleration. In most of the existing algorithms the along-track velocity is calculated by using the estimated Doppler slope (e.g. estimated with a matched filter bank or time-frequency analysis) under the implicit assumption that the across-track acceleration is very small and therefore negligible. Since we want to monitor real and more complex traffic scenarios with a future space-based traffic monitoring system like TRAMRAD, we must know which target accelerations we have to handle in reality. For this reason a car was equipped with an inertial measurement system (IMU) and differential GPS to measure accelerations in all three dimensions during rush-hour traffic. In this paper the results of the acceleration measurements are presented and discussed. The measurement results show that a substantial part of the observed accelerations is significantly higher than 0.1 m/s2. A theoretical analysis (which is verified by detailed simulations) of the Doppler slope shows also that at such higher across-track accelerations a reliable estimation of the along-track velocity by means of a Doppler slope analysis is unemployable in practice. Finally, some basic ideas are presented which overcome this ambiguity problem and enable a reliable separation between along-track velocity and across-track acceleration.