What does shaking when accelerating mean? Please help!

The 'bucking' is not good, to state the obvious. Grinding is gears not meshing, you may have broken a cog off of a gear, so yes it is probably the transmission

define vibration when you accelerate? Like 0-60 or in a specific gear? This shift put stress on alot of components. IDK how fast you were going but unless you were racing it, or in 5th cruising there may not be internal damage. The trans usually wont engage a gear when going to fast for it without some effort on your part.

I was only going like 40, it wasn't even fully in second gear, it hit into a place like in between 2nd and 4th, and when I heard the sound I put it in nuetral so it's not like the gears were grinding for a long time

So define this vibration on acceleration you feel. Is it from a stop? If you did what you said your gearbox should be fine. A shakeing from take off can be worn cv axles.

I would be looking at the inner drivers on the axle shafts.

it only really happens in third and fourth gear when the tacometer gets to about 2 wile in third gear and then i shift to 4th gear and it gets worse. it seems to be the worst when its going uphill, the vibration is mostly in the petals and the dashboard where the stereo is

I’ve same issue in a 1.9 tdi I hit a pothole tho not grinding any gears but I’ve the vibration issue I think it’s either the cv joint or the shafts or else engine mounts anyone help me it’s a Jetta mk3 basically a mk5 golf. 2006. 105bhp mapped to 160 bhp.

I was going 60 as I was going uphill it started shimming or shaking a little kind of like the gas is not getting through. Also some times when I Excelerator the RPMs go up but the car is not going any faster

Also my cars a 2006