How motion curves shape time perception in progress bars: A Bayesian adaptive psychometric approach

This study quantitatively examined users' time perception of progress bars controlled by different motion curves using an adaptive Bayesian psychometric approach (Quick Estimate of Slope and Threshold-QUEST). User interface (UI) animations incorporate various motion curves, particularly variable-speed forms such as slow-down, speed-up, Bézier, and elastic curves. Despite their widespread use in modern UI design, limited empirical evidence exists regarding how they influence perceived duration. To investigate how different motion curves influence users' duration perception, we measured the point of subjective equality (PSE) between constant-speed and four 5-s variable-speed progress bars. In each trial, participants compared a constant-speed progress bar with a variable-speed progress bar and judged which appeared shorter in duration. The QUEST algorithm adaptively adjusted the constant-speed bar's duration based on individual responses across 40 trials to estimate the PSE. Eye-tracking data were also collected. Results indicated that constant-speed and speed-up progress bars were perceived as shorter. The findings suggest that the final phase of a progress bar may play an important role in subjective time perception, potentially reflecting end-phase attentional processes and anchoring-related judgment effects. Eye-tracking results indicated that longer perceived durations were associated with lower eye blink rates, suggesting stronger attentional engagement and blink suppression during viewing. Based on the research findings, when perceived waiting time is a critical dimension of user experience, designers may benefit from prioritizing constant-speed or speed-up motion curves in animation design. The study also adds to time perception research by showing how subtle visual dynamics can shape users' temporal judgments in interactive contexts.