how do i know if my motor mounts are bad?

Hello, vibration on acceleration is almost never related to a motor mount issue. The type of vibration is what should be determined first, such as rhythmic dependent on engine speed, rhythmic depending on vehicle speed, or erratic. Once that is determined, then a diagnostic process can be undertaken to determine the source of the problem. Regarding your alternator pulley -- I cannot think of a reason that the pulley itself could be "bad" - why do you ask?