Why is my Car makes a jerking sensation when accelerating to 20mph?

Transmission fluid should be changed periodically, but I don't think changing your fluid will be key in solving this concern. I can't even say it's transmission related. It could be engine performance related. Hands on testing is required to see what's going on when the problem occurs, by way of monitoring performance with a diagnostic tool when it happens. It's something a shop near you could possibly drive with you and experience the concern -- then give you advice on best next steps. Use this link to find some shops near you that can help with your concern: www.repairpal.com/repair-shops