2016 4th gen prius engine mount broken

welcome!
wouldn't it give you trouble all the time if it was an engine mount?

5-signs-need-replace-engine-mounts

tech-tip-motor-mount-inspection-guidelines

3-signs-of-a-bad-motor-mount

 

Highly unlikely that it is the engine mount. More than likely (based on your description and mileage) it is the EGR system giving you problems. The noises when braking are more than likely brake issues.
So basically, a good news/bad news situation.

 

Yes it's likely a engine mount is going bad. Mine has the same symptoms and vibrates at pretty much all RPM's and when in park. I tested it by running the engine in park and raising the engine up a bit from the oil pan (with small 2x4 wood), and sure enough the vibration disappeared. This video shows this:

Will be replacing the engine mounts very soon.

 

Perhaps you can explain why the OP experiences it only on a cold start and why the Car Care Nut claims that the symptoms the OP describes is NOT the engine mount?

 

Fourth gen EGR has proven pretty bullet proof. Fourth gen head gasket failures have been reported here, due to coolant loss through exhaust heat recovery system.

 

Yes agreed Mendel. My 4th gen's EGR at 260k was quite clean and can see through it well.

For 3rd gen, if there's the "rattle", most likely it's a bad HG. As for the motor mounts, I would replace them all after 250k miles regardless of the generation.

 

Very true. However, based on what the symptoms the OP describes, especially intermittent vibration, and only under certain conditions (which happen to match what The Car Care Nut described), I certainly doubt a broken motor mount, especially on a 4th Generation Prius, barring any extreme damage that wasn’t mentioned, such as trying to drive it like The General Lee in Dukes of Hazard !

I seriously doubt a stock Prius could generate sufficient torque to cause such damage, and playing Dukes of Hazard would very likely cause significant other damage to the point that mounts would be the least disruptive!