(Originais Teachy 2023) - Question Very Hard of Physics

A Formula 1 car is completing a circular curve on a race track with radius R and constant centripetal acceleration a. At point A of the curve, the car is moving with an angular velocity ωA around the center of the curve. Given that the centripetal acceleration is v^2/R and angular velocity is related to linear velocity by the equation v = ωR, where v is the linear velocity and R is the radius of the curve, determine the mathematical expression relating the linear velocity at point A, vA, with the angular velocity ωA and the radius of the curve R. Considering that the car starts from rest and accelerates uniformly until reaching the angular velocity ωB after traveling half of the curve, where ωB > ωA and the angular acceleration α is kept constant throughout the journey to point B, determine the expression for the angular acceleration α in terms of ωA, ωB, and R. Your answer should take into account the conservation of energy and provide the theoretical justification for the expression found.