Scanning line optical tweezers are a powerful tool for the study of colloidal or biomolecular systems in the low-force regime. We present a fast, high-resolution particle position measurement scheme that extends the capabilities of these instruments into the realm of dynamic measurements. The technique is based on synchronous detection of forward-scattered laser light during a line scan. We demonstrate a position resolution of better than 50 nm for bandwidths of as much as 40 kHz for pairs of microspheres trapped in a flat line potential at center-to-center separations of 1.7-6 microm.