Sphere falling through viscous material - velcoity calc

[Bakery87]

I'm dropping a sphere from a known height, and it enters a viscous fluid. I know the initial velocity as it enters the fluid, from there I need the velocity as it falls through the fluid (as a function of time).

I know it should approach it's settling velocity (terminal velocity) and from there I can use stokes law to get the terminal velocity. What I need is the velocity as it approaches that point. Assuming no spin of the sphere. I know the fluid's density and viscosity, sphere density, and initial velocity as it enters the fluid.

I can find this equation for a skydiver falling through the air, but since the air has very little viscosity it does not contribute to the buoyancy of the skydiver.

 

[zorro]

You don't think about terminal velocity from the start. Just find out the velocity as a function of time. I remember there is an exponential term in it. If you substitute t as infinity in the equation, you get the terminal velocity.

Hint- Its acceleration will not be constant. From Newton's second law Fnet = ma, here a=dv/dt.