A car starts from rest on a horizontal circular road of $190\ \mathrm m$ and gains speed at a uniform rate of $1.2\ \mathrm{m/s^2}$. The coefficient of static friction between the tyres and the road is $0.37$. Calculate the distance travelled by the car before it begins to skid.
Here is my doubt regarding the solution and the problem statement too.
As the solution given in the picture above, we can see that they have considered the centripetal force and the tangential force. But if I observe from the frame of the car,then centrifugal force applies for me. Then the direction of the net force is becoming different,so is the solution wrong?
Also this is kind of contradictory because if that happens there is no resultant force in the inward direction and so there is no force to balance the centrifugal force,so this is a huge dilemma at hand.So how will the net force be defined in this system?
Is this free body diagram even correct? I look forward to the brilliant answers of all the physics lovers out there to this question.