if the motor mount is bad will it cause the car to jerk lack hesitation

yes

used to be a big deal with the mechanical connection...nowadays doesn't quite do this anymore like it used to...suspect a bad TPS (throttle position sensor)~ if in doubt take a floorjack and jack up the motor, if the mounts separate, replace them~

The car is a front wheel drive. You might feel the engine thud as it moves in the mounts. It's easy to check the mounts. Open the hood, push the brake and move the gear shift from "Drive" to "Reverse" and back. If the mounts are loose, you can see the engine shift around.