The phrase "accelerating forward" is correct and usable in written English.
It can be used in contexts where you want to describe the action of moving ahead or increasing speed, often in a metaphorical sense as well.
Example: "The company is accelerating forward in its efforts to innovate and lead the market."
Alternatives: "moving ahead rapidly" or "gaining momentum."
While corporations and legislators were moving the goal posts back, technology was accelerating forward.
When the driver tried to dislodge the Mercedes by accelerating forward, the car moved only slightly on the bonnet and seemed to further damage the Ferrari.
Of experience and talent unbound and accelerating forward beyond the valley of our own experience and into every corner of the world.
For example mec-4 and mec-10 worms fail to respond to a light touch applied manually with an eyelash, while wild-type worms will respond by accelerating forward or backward depending on the placement of the stimulus.
He added, "What we have done is accelerate forward, in a self-inflicted manner, the numerator.
The whole landscape was trying to accelerate forward, toward the tornado, while Sutton tried to back away.
The boat is accelerated forward on the drive, when the rower pushes against the oar handles by applying pressure with the leg and back muscles.
Johan Elmander lost possession inside the Stoke half and, when the ball was transferred to Walters, the striker accelerated forward before cutting inside Mark Davies and curling a sublime low shot inside Jaaskelainen's far upright.
Footage from Tensing's body camera showed that immediately after the officer fired, DuBose's vehicle indeed accelerated forward, eventually halting when it crashed into a utility pole farther down the street.
As a result, I became addicted to the sprint along the gutter, the leap on to the platform (observed by the impassive conductor), and then the G-force pull as the bus accelerated forward, my fist furiously gripping the pole.
As Mr. Anderson staggered along a grassy strip at the edge of a parking lot, a teenager driving a Ford pickup truck backed up and then accelerated forward, running over and killing him, the investigators said.
