The paper addresses acoustic vehicle detection and speed estimation from single sensor measurements. We predict the vehicle's pass-by instant by minimizing clipped vehicle-to-microphone distance, which is predicted from the mel-spectrogram of input audio, in a supervised learning approach. In addition, mel-spectrogram-based features are used directly for vehicle speed estimation, without introducing any intermediate features. The results show that the proposed features can be used for accurate vehicle detection and speed estimation, with an average error of 7.87 km/h. If we formulate speed estimation as a classification problem, with a 10 km/h discretization interval, the proposed method attains the average accuracy of 48.7% for correct class prediction and 91.0% when an offset of one class is allowed. The proposed method is evaluated on a dataset of 304 urban-environment on-field recordings of ten different vehicles.