Chadwick measured proton velocity in the polonium-beryllium experiment by likely accelerating protons through a voltage, using the relationship K=qV to determine kinetic energy. The charge of the protons and the applied voltage allowed for calculations of their drift velocity. Additionally, the deflection of particles in a magnetic field could be analyzed using the Lorentz force equation, F=qvB*sin(x). While the exact methods are debated, the principles of voltage acceleration and magnetic deflection are central to understanding proton behavior in this experiment. Overall, the discussion highlights the complexities in accurately measuring proton velocity in nuclear experiments.