A particle is revolving in a circle of radius 1 m with an angular speed of 12 rad/s. At t = 0, it was subjected to a constant angular acceleration `alpha` and its angular speed increased to `(480pi)` rotation per minute (rpm) in 2 sec. Particle then continues to move with attained speed. Calculate
(i) angular acceleration of the particle,
(ii) tangential velocity of the particle as a function of time.
(iii) acceleration of the particle at t = 0.5 second and at t = 3 second
(iv) angular displacement at t = 3 second.