Tach is bouncing at 3800 to 4000 rpm

I own a 2006 mustang v6 manual. I have never had a problem with my vehicle but my wife was hit from behind and now it makes a rattle under the car when I let off the gas or rev the engine. Well, tonight it worked fine on my way home but when I got back in the car to drive I noticed the car tach when I rev will not go over 4000 rpm and will bounce. When I drive it’s like there is no power to accelerate (sputter cuts in and out) and I really can’t go past 25-30 mph. After I reved the engine at the said 4000 rpm bounce for a few seconds there is a odor (unknown smell but almost a burnt smell)

The strange rattle metal sound Seems like it is coming from under the car about the drivers/passenger seats, but who knows. It’s just my observation. Tranny is shifting into gears fine and idel is fine

Any ideas help… I’m gonna look at it tomorrow. I need some direction on where to start

Probably a loose heat shield causing the rattle. The other problem has so many options, any error codes?

No power from the engine could be a symptom of a plugged catalytic converter or a restriction in the exhaust system. Check underneath the car for any damage to the exhaust system from the accident. If an exhaust pipe got bent it could restrict the exhaust and prevent the engine from making full power.

No check engine light showing even with the rpm issue… I have a feeling it could be an issue with the cat… I bet when she got hit it pushed the exhaust and damaged the cat… Can a bad cat cause these issues with rpm and exceleration problems?

It can absolutely affect power if the cat, muffler, or pipes were damaged in a way that obstructs exhaust flow.