AM radio noise when brakeing/excelerating

That's like asking "do you get wet when walking in the rain?"

Any AM radio will have static on it.
AM is prone to interference by its very nature. AM is amplitude modulation. Anything can change the apparent modulated amplitude, including noise imposed over it from anything that generates electromagnetic noise. That includes power lines, generators, motors, inverters, arc lamps, lightning, etc.

 

It seems that if you have had the radio replaced they must have checked the antenna but this sure sounds like an antenna or antenna cable problem to me. DanMan32 is right AM is prone to noise of all types, but so is FM if you have a weak signal.

I have noticed the radio in my Prius seems as good as any car radio I have had and I can receive a good strong AM station at quite a distance. The point being the Prius seems to have a good radio so I think you have something broken somewhere, which you probably knew to start with.

I would check the antenna, the coax between the antenna and the radio, the power and the ground connections. If all that stuff is OK you might be able to pull the radio and take it to an electronics shop (if you can find a good one that won't rip you off) and have them check the sensitivity, selectivity, etc. Then you would know if the problem is in the radio or somewhere else in the car.

If you have already lost two radios I think the power to the radio should be checked with the car powered up and also with it in accessory mode. I think it's important to check both because with it in the accesory mode it most likely runs the radio off the 12 Volt aux battery, when powered up it runs off of a 12 Volt output of the inverter.

good luck

 

Check the antenna amp as well.
Make sure it gets its turnon from the HU, which may be all the power it gets (no constant 12+ to it like the rest of the modules in the car). Also make sure the antenna connections do route through it.