When a fast dust particle hits a spacecraft, it generates a cloud of plasma some of which escapes into space and the momentary charge imbalance perturbs the spacecraft voltage with respect to the plasma. Electrons race ahead of ions, however both respond to the DC electric field of the spacecraft. If the spacecraft potential is positive with respect to the plasma, it should attract the dust cloud electrons and repel the ions, and vice versa. Here we use measurements of impulsive voltage signals from dust impacts on the Parker Solar Probe (PSP) spacecraft to show that the peak voltage amplitude is clearly related to the spacecraft floating potential, consistent with theoretical models and laboratory measurements. In addition, we examine some timescales associated with the voltage waveforms and compare to the timescales of spacecraft charging physics.