Drift speed of electrons when the object is grounded So I know that the drift speed of electrons is usually pretty slow. Let's say I have a charged sphere and I would ground it over a wire. How fast would the electrons leave the sphere? Would that drift speed be a lot faster than usual? I just want to get the general idea of the speed.
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So I know that the drift speed of electrons is usually pretty slow.

Yes, if $10A$ of current is maintained in a conductor of cross-section $10^{-4}m^2$, with number density of electrons equal to $9X10^{28}m^{-3}$, drift velocity of free electrons will be $0.000006ms^{-1}$ (with the centimeter scale in your geometry box, it will be $0.0006cms^{-1}$).  

Let's say I have a charged sphere and I would ground it over a wire.  

By this, I hope you mean connecting the charged sphere to the ground with the help of a conducting wire. 

How fast would the electrons leave the sphere?   

We can't always say that electrons leave the sphere, if sphere is positively charged, electrons flow from earth to the sphere. Because, earth is neutral and sphere is positively charged. If sphere is negatively charged, electrons flow from sphere to the earth, in that case drift velocity depends on many factors, such as charge on the sphere, potential difference, etc.  

Would that drift speed be a lot faster than usual? I just want to get the general idea of the speed.

I would just say that drift velocity in your case will constantly decrease with the flow of charge. I am unable to say you the exact or approximate value of drift velocity because of unavailability of data. But you can have general idea with the example given in the first paragraph.  
