In this paper, we propose a time and memory efficient Ultra Wide Band Short Range Radar (UWB SRR) system for measuring relative target velocities of up to 150km/hr. First, for the proposed detector, we select the required design parameters for good performance. The parameters are the number of coherent integrations, non-coherent integrations, and FFT points. The conventional detector uses a Fast Fourier Transform (FFT) to extract the range and velocity of the target simultaneously. Therefore, it requires high computation effort, high FFT processing time, and a huge amount of memory. However, the proposed pulse radar detector first decides the target range and then computes the target velocity using FFT sequentially for the decided range index. According to our theoretical and simulation analyses, the FFT processing time and the memory requirement are reduced compared to those of the conventional method. Finally, we show that the detection performance of the proposed detector is superior to that of the conventional detector in a background of Additive White Gaussian Noise (AWGN).