The Metro-North train involved in Sunday’s horrific disaster derailed on a 30-mph curve because it was traveling at 82 mph, authorities revealed Monday.

Engineer William Rockefeller told investigators that he had zoned out as the train was barreling toward the bend — and that he was jolted back to reality only after a whistle went off warning him he was going dangerously fast, sources told The Post.

“He was just somehow inattentive,’’ and as soon as he realized what was happening, he jammed on the brakes, one source said.

But it was too late.

According to data from the train’s two “black box” recording devices, Rockefeller didn’t apply the brakes until just five seconds before the derailment.

The train’s throttle, or gas lever, was first thrown into the “idle” position, similar to putting a car in neutral, a source said.

A second later, the brakes were slammed. But it wasn’t enough to the seven cars and push locomotive from jumping the tracks and rolling toward the Harlem River.

One theory investigators are looking into is the possibility that Rockefeller had fallen asleep prior to the derailment.

Another area of concern is that Metro-North trains are not equipped with a system called PTC or positive train control that would have applied the emergency brakes in the event that the operator was unable to.

“If the engineer fails to slow down, it will provide an alarm and if he fails to brake, it will apply the emergency brakes,” one transit source said.

The holiday-weekend wreck left four dead and 63 injured just north of the Hudson Line’s Spuyten Duyvil station in The Bronx.

Rockefeller immediately admitted zoning out to investigators at the scene Sunday, a law-enforcement source said.

He also suggested the train’s brakes had “failed to engage.’’

Investigators asked him, “Were you drinking?’’ a source said.

The 46-year-old married engineer didn’t smell of alcohol and adamantly denied he had been boozing, the source said.

The National Transportation Safety Board, which is heading the investigation, is awaiting a toxicology report.

Authorities confiscated Rockefeller’s cellphone to see if he had been texting or talking on it.

The NYPD and Bronx District Attorney’s Office have launched their own joint criminal probe and will also look at texting and drugs and/or alcohol as possible factors, sources said. They’ve subpoenaed his phone records.

While Rockefeller chatted with law-enforcement Sunday, he was less talkative Monday, the source said.

“They found him elusive and traumatized,” the source said.

NTSB member Earl Weener noted Monday that the train was speeding even before the curve, traveling 12 mph faster than the maximum limit of 70 mph in the straightaway along the Hudson River.

“At this point, we are not aware of any problems or anomalies with the brakes,’’ he added.

Multiple sources familiar with the operation of Metro-North trains suggested that wet leaves on the tracks this time of year might have played a role — but law-enforcement sources scoffed.

Weener said the NTSB will probe how the brakes were operating earlier in the trip, which originated in Poughkeepsie.

The Grand Central-bound train was able to stop at nine stations before the derailment.

Sen. Charles Schumer said there were no problems with the tracks or signals.

As for the brakes, “clearly, [they] were working a short time before [the train] came to this curve.

“When I heard about the speed, I gulped,” he said. “For a train to be going 80 mph around at curve is just a frightening thing. It raises so many questions.”

Still, he added, “it’s premature to blame anyone or anything right now.”

Investigators were seeking surveillance video, but so far only have a “low-quality” feed from a bridge, which has been sent to Washington, DC, for enhancement.

As for the data collected so far, “It tells us what happened; it doesn’t tell us why it happened,” Weener said.

Anthony Bottalico, an official with the ACRE Local Division 1 rail-employees union, called Rockefeller, a 20-year MTA veteran, “a man of fine character and sincerity.”

“He is a quality engineer. He is well respected. He has an incredible work ethic,” Bottalico said.

“He’s very traumatized right now . . . He hasn’t slept in over 24 hours. He suffered some problems with his lower back. He got knocked around pretty good.”

“Yesterday, a little piece of everyone on the railroad died,” Bottalico said. “We are there for him.”

He added the engineer would “fully cooperate” with the probe.

Emergency workers remove a body from a derailed Metro-North train in The Bronx. At least four people were killed and more than 60 injured when the speeding train slammed into a curve and ran off the rails Dec. 1. John Roca The scope of the devastation in the aftermath of the deadly train derailment. AP Officials at the grisly scene where a body was found in the aftermath of the terrible accident. Theodore Parisienne The train's conductor, William Rockefeller, is taken away on a stretcher after the deadly crash. John Roca First responders treat the injured. William Farrington Firefighters use a device to transport victims along the rails. William Farrington William Farrington Reuters John Roca Officials remove a body from the scene of a Metro-North train derailment in The Bronx. Reuters AP AP AP A Metro-North train lies on its side after derailing in The Bronx. AP Emergency workers at the scene of the train wreck that killed four on Sunday. AFP/Getty Images Emergency rescue personnel work the scene of a Metro-North passenger train derailment. AP Injured passengers are removed from the derailed Metro-North train. William Farrington Injured people are tended to by first responders. AP A Metro-North passenger train derailed on a curved section of track in The Bronx on Sunday morning, killing four people, injuring 63 and coming to rest just inches from the water, authorities said. Reuters Reuters First responders view the derailment. AP Rescue workers search through a car at the site of a Metro-North train derailment in The Bronx on Dec. 1. Four were killed and 63 were injured. Reuters AFP/Getty Images Ad Up Next Close Happy end to fox tale: Missing critter found safe The sly red fox who burrowed her way out of... 26 View Slideshow Back Continue Share this: Facebook

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Sixty-three people were injured in the accident, which left rail cars overturned. At least seven remained critical at Bronx hospitals, including one dad who may be permanently paralyzed.

Mayor Bloomberg, who was playing golf in Bermuda when the accident occurred, flew back to New York and visited one female cop hospitalized with a broken collarbone.

A source said he was told immediately of the derailment, yet spent several more hours on the links with his girlfriend and one of his daughters.

“The question for us, I think, in any emergency situation, is whether government agencies perform well,” he said Monday. “The response by the men and women in uniform was outstanding.”

Additional reporting by Jamie Schram, Laurel Babcock and Frank Rosario