A car starts from rest on a curve with a radius of 190m and accelerates at 0.600m/s^2 . How many revolutions will the car have gone through when the magnitude of its total acceleration is 3.50m/s^2 ?

Question

A car starts from rest on a curve with a radius of 190m  and accelerates at 0.600m/s^2  . How many revolutions will the car have gone through when the magnitude of its total acceleration is 3.50m/s^2  ?

drwls · Answer

You will need to consider both centripetal aceleration (a_r) and tangential acceleration (a_t), which are perpendicular.
3.50 = a_t^2 + a_c^2 = a_c^2 + 0.36
a_c^2 = V^2/R = 3.14 m/s^2

Solve for V when the acceleration of 3.50 m/s^2 is reached. From that, get the time and the number of revolutions