Q: My car will not get over 20 mph. What is wrong?

The battery replacement seems to be a coincidence and has no bearing on the symptom you are experiencing. The only exception to this would be if during the battery replacement, any essential wiring was disconnected or damaged, such as the wiring to any electronic throttle sensors or controls. Initially, I would recommend using a code scanner to see if any diagnostic trouble codes have been set. You can do this yourself or have a certified technician do this for you with an inspection. If no codes have set, the mechanic would check and see if the transmission is stuck in first or second gear, in which case the diagnostic would focus on the transmission controls including things like the shift solenoids, the valve body, and so forth. If there is nothing wrong with the transmission, the problem you are describing is likely due to a fault in the air induction system, the fuel supply, or the ignition system, although there is a possibility that a mechanical issue involving valve timing could cause this sort of symptom as well. A professional technician, such as one from YourMechanic, can diagnose your difficult acceleration problem to get to the root of the issue and then let you know of your repair options.