A car starts from rest on a curve with a radius of 160 m and accelerates at 1.80 m/s^2. How many revolutions will the car have gone through when the magnitude of its total acceleration is 2.20 m/s^2?

the angular acceleration is 1.60/160 in radian/s^2

I don't see how anything can be solved without know how long it accelerated at this acceleration.

Displacement is a function of time, and acceleration.