Car won't accelerate properly sometimes.

I drive an old 2001 Ford Taurus 3.0L that has had an issue lately. I find that it doesn't always accelerate properly after turning it on. I step on the gas and it only goes 10-20 mph at most until I reach 3 RPMs (on the gauge), after which it'll speed up quickly and then drive normally afterwards without much issue. I get the feeling it has to do with the transmission, and the only thing I can really check myself is the fluid, which looks fine and not especially dark or dirty.