The passenger inside the car is in the reference frame of the car so he experiences centrifugal force

= m${{v}^{2}}$/r acting on the car. So, to remain in circular path force should be larger as it is proportional to ${{v}^{2}}$ For an observer on the road side finds that the centripetal force m${{v}^{2}}$/r acting on the car becomes inadequate with increases in v. Since again r is insufficient so the car skidded