(A) Predicted speed profiles for a walking bout of ten steps, comparing minimization of Energy and Time (Energy-Time, solid line) against maintaining steady speed (min-COT, dotted line) or steady acceleration and deceleration (steady accel, dashed line). Energy-Time minimizes the total push-off (PO) work plus time expended for a walking bout, for a model with pendulum-like legs (inset). Steady min-COT walks at the steady speed that minimizes cost of transport, by accelerating immediately to that speed. Steady acceleration walks with linearly increasing speed until mid-point, then decelerates linearly back to rest. Energy-Time predicts a gently rounded speed profile, min-COT a trapezoidal profile (always at min-COT speed), and steady acceleration a triangular profile. Speeds are discretely sampled as the average forward speed over each step (filled dots), starting with an initiation impulse to accelerate from standing and a termination impulse to decelerate at the end (gray dots). (B) Positive work inputs for each hypothesis, including initiation work (gray dots) and push-off work (colored dots, one per step). Energy-time hypothesis predicts the least total work (inset bar graph compares Energy-Time "E-T", min-"COT", steady-"accel" costs). Predictions are for a dynamic walking model with pendulum-like legs (inset, see Methods). All predictions are designed for the same duration based on steady min-COT speed as a reference, resulting in cost of Time . Predictions are plotted in terms of normalized units based on body mass , leg length , and gravitational acceleration ; scale for typical human also shown, mass 70 kg, leg length 1 m.