Answer
$1.84 \frac{m}{s^{2}}$.
Work Step by Step
Choose up to be the positive direction. Newton’s second law tells us the required net force in the vertical direction.
$$\Sigma F=F_t – mg = ma$$
$$a = \frac{ F_t-mg}{m} =\frac{163 N-(14.0 kg)(9.80 \frac{m}{s^{2}})}{14.0 kg} \approx 1.84 \frac{m}{s^{2}}$$
The answer is rounded to 3 significant figures. It is positive so the acceleration is upward. 163 N exceeds the weight, so the bucket is being lowered vertically, but slowing down.
