A 15.0 kg bucket is lowered vertically by a rope in which there is 188 N of tension at a given instant

2.72 m/s²

Explanation:

F = m(g + a)

188 = 15.0(9.81 + a)

188 = 147.15 + 15.0a

40.85 = 15.0a

a = 2.7233333... ≈ 2.72 m/s²

This is an upward acceleration as the force being applied is greater than that needed to maintain constant velocity. (147 N)

So even though the bucket is being lowered, it's rate of descent is decreasing  with time. If the acceleration continues for long enough, the bucket will begin to rise.