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The phrase "accelerated towards" is correct and usable in written English.
It can be used to describe the action of moving quickly in the direction of something or someone.
Example: "The car accelerated towards the finish line, leaving the other competitors behind."
Alternatives: "rushed towards" or "sped towards".
Exact(60)
This force is an observable in the sense that a unit test mass at r will be accelerated towards the central mass by this force with acceleration F. The potential field U becomes more negative as r gets smaller.
"Anderson, you cunt," he roared as he accelerated towards Bruce.
From inside his own half, the Chelsea player accelerated towards goal as Canada backed off.
"England performed their U-turn on the road to perdition and accelerated towards redemption at breakneck speed".
He cleverly anticipated Ramires's poor pass, out-muscled Alex, accelerated towards goal and finished smartly passed Henrique Hilário.
The mephedrone political crisis accelerated towards its climax after the deaths of two Scunthorpe teenagers who police said had taken mephedrone.
It was joyous, thought-provoking, passionate, stirring, charming and beauteous; but it had edge too, which hardened and accelerated towards the end.
At Villa, talk of the tomb is premature, and yet there is a reason the club has long since outstripped the disrepair of its environs and accelerated towards desperation and decay.
In this method, powder is introduced into the flame, melted and accelerated towards the workpiece.
As the driver approached a second checkpoint he accelerated towards two gendarmes, one of whom opened fire.
Through inert carrier gas, powder feedstock is introduced and accelerated towards plasma jet which is further directed towards workpiece.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com