Most of these sort of things work in a similar way to mobility scooters, cordless drills, etc.
The motor is generally a dc permanent magnet motor that will run in either direction depending on the polarity of the connections to it. Reversing the polarity and therefore the direction of rotation is accomplished by a switch - with a cordless drill the switch is a manual mechanical switch while a mobility scooter the task is accomplished by relay(s) and semiconductor devices on the circuit board depending on which part is energised by the handlebar control.
I expect your kid's quad bike is similar in principle. In my limited experience the quality of the internal circuitry, the wiring, connections and switching is usually well below what it should be - if you are lucky, you will find a wire has fallen off but the problem could be more complex.
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Most of these sort of things work in a similar way to mobility scooters, cordless drills, etc.
The motor is generally a dc permanent magnet motor that will run in either direction depending on the polarity of the connections to it. Reversing the polarity and therefore the direction of rotation is accomplished by a switch - with a cordless drill the switch is a manual mechanical switch while a mobility scooter the task is accomplished by relay(s) and semiconductor devices on the circuit board depending on which part is energised by the handlebar control.
I expect your kid's quad bike is similar in principle. In my limited experience the quality of the internal circuitry, the wiring, connections and switching is usually well below what it should be - if you are lucky, you will find a wire has fallen off but the problem could be more complex.