Angular velocity after time t seconds = 4t rad/s

i.e. tangential velocity v = 4rt m/s where r is the radius of the circle .

So, the tangential acceleration = 4r m/s²

now, v²/r = 4r

i.e. 16rt² = 4r

t = 0.5 second

Sorry for not writing the units.

Given, angular accn (aa) = 4

        So, at any instant, tangential acceleration = Radius * aa

                                                                                   = 4R

              Now after any time t, angular velocity = 0+4t = 4t

                                                   => Linear velocity(v) = Radius*Angular velocity = 4Rt

                                                   So, centripetal accn = v² /R = 16Rt²

                                                          According to question, 16Rt² = 4R => t = 1/2 sec