heater blower issuess

My heater blower works on and off, sometimes it will not come on at all, other times it will just start running after I have been driving for a bit, It does not matter what position the switch setting is on, I have also noticed that sometimes while not turning the ignition key all the way to start the car but just to turn the radio on, the motor will start off real slow, than gradually speed up to normal :disappoin

Please advise.

brushes in the blower motor are wore down. replace motor.