The mechanisms of perceptual decision-making are frequently studied through measurements of reaction time (RT). Classical sequential-sampling models (SSMs) of decision-making posit RT as the sum of non-overlapping sensory, evidence accumulation, and motor delays. In contrast, recent empirical evidence hints at a continuous-flow paradigm in which multiple motor plans evolve concurrently with the accumulation of sensory evidence. Here we employ a trial-to-trial reliability-based component analysis of encephalographic data acquired during a random-dot motion task to directly image continuous flow in the human brain. We identify three topographically distinct neural sources whose dynamics exhibit contemporaneous ramping to time-of-response, with the rate and duration of ramping discriminating fast and slow responses. Only one of these sources, a parietal component, exhibits dependence on strength-of-evidence. The remaining two components possess topographies consistent with origins in the motor system, and their covariation with RT overlaps in time with the evidence accumulation process. After fitting the behavioral data to a popular SSM, we find that the model decision variable is more closely matched to the combined activity of the three components than to their individual activity. Our results emphasize the role of motor variability in shaping RT distributions on perceptual decision tasks, suggesting that physiologically plausible computational accounts of perceptual decision-making must model the concurrent nature of evidence accumulation and motor planning.