Hi I have a 2008 infiniti g35 and im noticing when I drive and I get under alight my car will jerk when pressing down on gas.

 

 

Wow the title made me giggle.

Gotta get my mind out of the gutter.

 

You must not be giving your car enough attention if it feels the need to jerk around with you right there.

 

 

A serious answer to your original post, your rear differential bushing is probably 100% torn to pieces, you can Google search about a billion threads on this problem it's by far the most common thing to wear out on the G35. Replace it with a polyurethane one, they cost about $100 and it takes half a day if you've never done one before. There's plenty of threads on how to do it as well as tons of videos on YouTube so you know what to check for to verify its shot.

Youay also have motor mounts or transmission mounts that are worn, tranny is a piece of cake, motor is a total pita.