You’re using this phrase wrong, E.L. You can’t just use ‘with terminal velocity’ to mean ‘really really fast’. An object moves at its terminal velocity when it’s falling, for one. To quote Wikipedia, “A free-falling object achieves its terminal velocity when the downward force of gravity equals the upward force of drag. This causes the net force on the object to be zero, resulting in an acceleration of zero.”
So not only would your elevator have to be falling instead of rising (is the reception desk on the fiftieth floor? Is the twentieth floor underground? Is it really the negative-twentieth floor?), it would have to be falling for long enough for air resistance to balance with gravity. It would also be falling at terminal velocity, not with terminal velocity. Terminal velocity is a specific velocity. For example, the terminal velocity of a human being is about 176 feet per second. You don’t say someone is driving with 30mph, you say they’re driving at 30mph.
Now, I don’t know enough physics to calculate the terminal velocity of an elevator, but given how massive an elevator is in comparison to a person, I am willing to bet it’s pretty fast.
Of course, it’s quite possible that you just didn’t know what the phrase meant. That could be it too.