Usually when a car makes squealing sound after accelerating with the heater on, the serpentine belt is a little loose. It likely needs adjusting by a professional.
Loose belt -- replace or lubricate ADD-ON If it is a metallic squeal that continues for a minute or so after the car starts it could be your water pump bearing. Get your mechanic to check it out and replace before you need a tow truck.
Timing Belt.... Check all your belts.
the heater controls are run on engine vacuum. When a engine is accelerating it has a drop in vacuum. There is a one way check valve that keep vacuum in the heater circuit that has gone bad. You could have it fixed or you can deal with it, its not that big of a deal
check and adjust belts
The squeal when you turn on the AC or heater is a loose fan belt. It may be cracked and need replaced, or it may just need tightened.
You may be hearing the coolant passing thru the heater core with an air pocket trapped in there.
noise and jolting is present whilst car is idolling and accelerating
Frame of reference is the measurement or observation that tells you that a car is accelerating. It uses the second law of motion to tell you rather or not the car is accelerating.
My car is accelerating at 10 miles per hour per hour.
At least inspect when you hear squeal. Base further work on what you see.
your car might be weak on accelerating because it isn't firing on all cylinders.
Frame of reference is the measurement or observation that tells you that a car is accelerating. It uses the second law of motion to tell you rather or not the car is accelerating.