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When doing a force balance in fluid mechanics, ##\sum F = D_t(mV)##. This equation typically results to the Navier-Stokes equations. I'm reading a the following problem:

For small particles at low velocities, the first (linear) term in Stokes’ drag law implies ##F = kV##, where ##k## is a constant. Suppose a particle of mass ##m## is constrained to move horizontally.

They then solve this equation for the particle's velocity by taking ##-kV = m\frac{dV}{dt}##. My question is, how do we know the acceleration term is ##\frac{dV}{dt}## instead of ##\frac{\partial V}{\partial t} + V \frac{dV}{dx}##?

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# When to use the material derivative?

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