What speed must a train operate at when given a "restricted speed" signal?

A "restricted speed" signal indicates that a train must operate at a speed that allows it to stop within half the distance visible ahead. This is crucial for ensuring safety when approaching areas where conditions may be uncertain, such as curves, stations, or track work zones.

Operating at a speed below 30 mph is the rule that provides engineers with a guideline to ensure they have ample time to react to any unexpected obstacles or signals. The 30 mph limit is significant because it typically allows for enough reaction time and stopping distance while still enabling the train to maintain reasonable operational efficiency.

In contrast, the other options do not align with standard operational practices defined by the LIRR. The option stating below 15 mph is too limiting in many scenarios, and suggesting that speed is determined arbitrarily by the engineer lacks the necessary structure provided by the defined speed limits. Additionally, a speed not exceeding 40 mph exceeds the safe operational standards set for restricted signals.

Thus, the correct answer reflects the necessary precautions and safety measures that must be adhered to when responding to a "restricted speed" signal.