One of the most primitive but elusive current-voltage (I-V) responses of a superconductor is when its supercurrent grows steadily after a voltage is first applied. The present work employed a measurement system that could simultaneously track and correlate I(t) and V(t) with subnanosecond timing accuracy, resulting in the first clear time-domain measurement of this transient phase where the quantum system displays a Newtonian like response. The technique opens doors for the controlled investigation of other time-dependent transport phenomena in condensed-matter systems.