We present a rapid-scan, time-domain terahertz spectrometer employing femtosecond Er:fiber technology and an acousto-optic delay with attosecond precision, enabling scanning of terahertz transients over a 12.4-ps time window at a waveform refresh rate of 36 kHz, and a signal-to-noise ratio of 1.7 x 10(5) / root Hz. Our approach enables real-time monitoring of dynamic THz processes at unprecedented speeds, which we demonstrate through rapid 2D thickness mapping of a spinning teflon disc at a precision of 10 nm/root Hz. The compact, all-optical design ensures alignment-free operation even in harsh environments. (C) 2016 AIP Publishing LLC.