Radar has become a key sensor in many advanced driver assistance systems (ADAS). Due to its excellent range and Doppler resolution, low cost, and robustness against environmental conditions, it is considered an attractive sensor for detecting and tracking vulnerable road users (VRUs). In this paper, we provide a theoretical analysis of the accuracy of radar based VRU detection and tracking systems, thereby focusing on a number of specific scenarios such as early detection and tracking of VRUs, a VRU crossing the road at constant speed in front of a vehicle, a VRU moving parallel to a vehicle, etc. More specifically, we derive the Cramer-Rao lower bound (CRLB) for position and velocity estimation of a moving target based on a sequence of noisy range, azimuth, and Doppler measurements taken from a moving ego-vehicle equipped with one or multiple radars. Not only does the CRLB serve as a benchmark to evaluate the performance of any practical tracking algorithm, it also allows to gain practical insights regarding the impact of the radar setup and configuration on the tracking accuracy in different realistic scenarios. Furthermore, we show that the generalized least-squares estimator (GLSE) achieves excellent performance when few measurements are available, and propose a novel active sensing (AS) application based on the CRLB where the radar configuration is optimized on the fly to improve either tracking accuracy or computational efficiency.