The teacher offered extra playtime as a carrot to motivate students to finish their homework.

carrot 的本义是"胡萝卜"，在这里用作比喻意义。在英语中常用"胡萝卜"象征"奖励、激励"，与"大棒"（惩罚）形成对比，表示用正面激励来鼓励某种行为。