In particle image velocimetry (PIV), small particles are seeded in the fluid to trace the velocity profile. Given that the hydrodynamic drag force on a particle is given by Stokes's law:
Fd = 6*pi*r*u*(Vf-Vp)
where u is the viscosity of the solvent, r is radius of the particle, V is the velocity of the fluid. Derive the velocity equation of a particle under a sudden (step) change in velocity.