Final answer:
Gently applying the brakes is least likely to cause flat wheels for a train, as it allows the wheels to continue rotating and distributes friction and heat more evenly compared to sudden braking.
Step-by-step explanation:
When considering which action is least likely to cause flat wheels for a train operator, it's crucial to understand the mechanics involved in the train-wheel interface. Applying brakes gently is the action that is least likely to cause flat wheels. This is because applying the brakes suddenly can create a localized flat spot on the wheel due to the intense friction and heat generated, which does not allow the wheel to rotate as it skids. Flat wheels can also occur due to sharp turns or improper tire (wheel) pressure; however, avoiding sharp turns or maintaining proper tire pressure will not directly cause flat spots in the same way sudden braking can. Having a smooth and controlled braking process ensures the wheels continue to rotate and spread the heat and friction more evenly, thus reducing the risk of creating flats.