A Long Island Rail Road train’s “erratic” movement just before it crashed in Brooklyn on Wednesday and concerns about the locomotive engineer’s health suggest sleep apnea may have played a role in the accident that injured more than 100 people, a federal source said Friday.

The source, who was briefed by the National Transportation Safety Board, said investigators had determined the train entered the terminal at 33 miles per hour and then slowed to 15 mph, as required, but “the last three minutes showed an erratic pattern of acceleration and deceleration.”

“It is these last three minutes that he [the engineer] does not remember,” said the source.

The source added that the train’s speed moments before the crash ranged from 2 mph to 10 mph. Investigators said the train struck a bumping block at the end of the tracks at more than 10 mph. The speed limit in that area is 5 mph, LIRR officials have said.

“If you even hit the bumper you’re supposed to do so at zero,” the source said.

More than 100 people on the train, which originated in Far Rockaway, were injured in the crash, none seriously.

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The federal source added that the train’s movement just before the crash and other factors have raised suspicion among investigators that the 50-year-old engineer, who has not been identified, suffered from obstructive sleep apnea — a disorder that can contribute to fatigue.

NTSB spokesman Peter Knudson said Friday it was too early to even consider a potential cause. He said investigators were still in “the first stage” of the probe, gathering evidence from the crash scene in Brooklyn’s Atlantic Terminal. He said the NTSB could issue a preliminary report as early as next week, but could take a year or more to make a final determination of the cause.

If the engineer is found to have sleep apnea, Knudson said, “that will certainly become part of the factual record. And whether that has any role in the probable cause of the accident, that’s something we’ll determine at that stage of the investigation.”

In two recent deadly commuter railroad accidents in the Northeast — October’s crash of a NJ Transit train in Hoboken and the December 2013 derailment of a Metro-North train in the Bronx — federal officials said the engineers had sleep apnea.

Those, and other accidents, have led federal regulators to push for sleep disorder testing of locomotive engineers. After the Metro-North derailment, which killed four people, the MTA began a pilot program to test Metro-North engineers for sleep apnea.

MTA spokesman Aaron Donovan said 51 of the 438 engineers tested in 2015 — or about 12 percent — were diagnosed with sleep apnea. They were allowed to continue operating trains while receiving treatment and regular screening for the disorder.

Although the MTA announced in April that it was expanding the program to include LIRR engineers, the LIRR has yet to hire a contractor to conduct the testing. Donovan said the MTA expected to award a contract “in the coming months.”

Donovan said the MTA was the first public transportation agency in the United States “to identify sleep apnea as something to be tested, monitored and tended to carefully.”

MTA board member Mitchell Pally said Friday the LIRR had been trying to get its testing program up and running “as quickly as possible.”

“You don’t want to take people out of work just on a whim. You want to make sure that the science backs up what you’re looking at,” Pally said. “You have to do it in a fashion that is fair and equitable to everybody.”