Why does my car go into Limp Mode after acceleration ?

This can be many things but I would start by serving the throttle body and running the trouble codes. Here are three guides to go over to gain information on the condition and how to fix it:

https://www.2carpros.com/articles/reduced-power-limp-mode

and

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

and

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Here is how to service the throttle body on your car. Check out the images (below). Please let us know what happens.