The phrase "as he accelerated" is correct and usable in written English.
It can be used to describe an action occurring simultaneously with someone increasing their speed, often in a narrative or descriptive context.
Example: "The car swerved dangerously as he accelerated down the winding road."
Alternatives: "while he sped up" or "as he picked up speed."
"Anderson, you cunt," he roared as he accelerated towards Bruce.
"It's good," he answered as he accelerated and my neck snapped back against the headrest.
As he accelerated, he noticed, to his left, an elk galloping toward him from the ridge.
"I'm a natural, baby," he said, as he accelerated into the balmy night.
There were to be six more, as well as two sixes, as he accelerated in the latter stages.
"This is why we do sitcoms in Queens!" he said, as he accelerated to fifty-five miles per hour.
As he accelerates past 8.5 miles an hour — his usual pace on the treadmill — he glimpses a blur of a downy, female arm flung out to block him.
And Davidson's delivery and infectious amusement are engineered to crank laughter, as he accelerates towards another old-as-Arthur's-seat punchline: "Book the wife in on Monday morning!"; "I beg your pardon, madam, but I can't think of anyone who'd fuck you twice!".
Behind the wheel of a getaway car after an uninteresting, irrelevant and almost botched robbery, the driver glides past obstacles and shakes off pursuers, slowing down as often as he accelerates and maintaining a steady pulse rate even as the soundtrack winds up the tension to heart attack levels.
Whatever, Djokovic is in danger of leaving our own Andy Murray floundering in his slipstream as he accelerates towards his goal of becoming the first world No 1 since Andy Roddick in February 2004 without a first name beginning with R. Murray and Djokovic, just a week apart in age, are friends and occasional practice partners.
