This is a nice question! In order to turn the car must be subjected to a centripetal force. This force "pulls" the car, and anybody inside it, towards the center of rotation. So instead of going straight, the car would have a curved trajectory.
From the point of view of any body moving on a curve an apparent force is experienced, the centrifugal force. The person in the car, for example, would feel to be pulled away from the center of rotation. This is just a relative point of view from inside the car. In reality the person would turn as the car is turning.
The centripetal force is the real force acting on the people inside the car. The centrifugal force is just an apparent force.
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