Optical sampling by cavity tuning (OSCAT) enables cost-effective realization of fast tunable optical delay using a single femtosecond laser. We report here a dynamic model of OSCAT, taking into account the continuous modulation of laser repetition rates. This allows us to evaluate the delay scan depth under high interferometer imbalance and high scan rates, which cannot be described by the previous static model. We also report the demonstration of remote motion tracking based on fast OSCAT. Target vibration as small as 15 µm peak to peak and as fast as 50 Hz along line-of-sight has been successfully detected at an equivalent free-space distance of more than 2 km.