If the second hand goes around smoothly, it won't have any acceleration just a constant velocity.
If it's one of those watches that delivers an impulse every second then the hand would move 1/60th of 360 degrees every second. In this case you could use the angular version of the distance equation and solve for a, but you'd have to consider that the second hand goes from 0 to some alpha, then from that alpha back to zero (starting and stopping).