Car jerking while backing up or at a stop

It sounds like the engine is misfiring have you installed new spark plugs recently? Here is a guide to help you give the engine a tune up I would service the throttle bore as well:

https://www.2carpros.com/articles/how-to-tune-up-a-car-engine

and

https://www.2carpros.com/articles/throttle-actuator-service

Please run down these guides and report back.

Cheers, Ken