According to the Physics Factbook, nerve impulses travel at speeds anywhere from 1 meter per second up to around 100 meters per second. Blue whales reach up to around 30 meters long.
For a full-size blue whale, this means that a nerve impulse to move the tail muscles could take from 0.3 seconds to 30 seconds to reach the tail. While I'd imagine factors such as myelination and other adaptations function to keep this closer to the 0.3 second measure above, this is still a best case scenario, and would certainly be a noticeable delay were it a human being.
Do large organisms experience meaningful delays when moving their most distant appendages?