A man carrying a bucket of water is walking on a level road with a uniform velocity. Does he do any work on the bucket while carrying it?

Since the velocity is uniform, the man exerts no net force on the bucket in the horizontal direction, i.e., the direction in which he carries the bucket. The only force he exerts on the bucket is against gravity and this force is perpendicular to the direction of motion, i.e. the angle q between the force and displacement is 90. Therefore work done is W = FS cos q = FS cos 90° = 0.