A system for the rapid-scan (RS) acquisition of time-resolved nonlinear spectroscopic signals, capable of femtosecond resolution over a range of tens of picoseconds, is presented. Operationally, the system is based on a magnetically driven, commercially available velocity transducer that continuously scans a probe delay line relative to a fixed delay line while data are recorded on the fly and in real time. A simple calibration and data time-scale linearization are carried out and tested on optical-heterodyne-detected optical-Kerr-effect measurements. These results are compared with data acquired with a detection system that is based on a stepped delay-line lock-in amplifier. It is found that the RS system is favorable in several areas of signal acquisition, including signal-to-noise ratio, acquisition time, spectral resolution in the Fourier-transformed data, and immunity to artifacts such as baseline distortions.