This is the 4124th most frequent Polish word.
biegiem
"Running" or "at a run."
Here, 'biegiem' is used as an adverb to describe the way the action of running was performed—quickly and energetically.
Biegiem przebiegł przez park, żeby zdążyć na autobus.
He ran through the park to catch the bus.
In this sentence, 'biegiem' again functions as an adverb, emphasizing that the participants moved to the finish line specifically by running.
Podczas zawodów, wszyscy zawodnicy ruszyli biegiem do mety.
During the competition, all participants ran to the finish line.
Here, 'biegiem' highlights the necessity of running as the chosen mode of movement due to haste.