"ever accelerated" is a correct and usable phrase in written English.
You can use it when you want to describe something that has increased in speed or intensity over a period of time. For example, you could say, "The popularity of this product has ever accelerated since its launch."
Innovation is progressing at an ever accelerating rate, but the pace of discovery has in some sense slowed.
With the cycle of "retro" styles ever accelerating, and the children of the previous decade hitting 30, we're just about due for a 90s revival.
It is a £3.2bn-a-year industry of ever accelerating creativity (lentil crisps! dehydrated kale dippers! "popped" chips!), with the maize-based, vaguely Mexican tortilla chip in the vanguard of this crumb-spattered revolution.
Clutching a brown envelope, filled with briefing notes rather than the folding kind to which the French lead financial prosecutor made such lurid reference later, Lord Coe had already read Dick Pound's second report and was ready to strike a more contrite tone as he sought to pull his sport and his IAAF presidency from an ever accelerating death spiral.
Large-scale data-intensive web services are evolving faster than ever, accelerating global growth in data usage and traffic at a rapid rate.
Tissue engineering is an ever accelerating field surrounded by excitement, fueled by need and on the cusp of changing medicine as we know it.
All current computer and networking systems suffer from missing elements that could enable the integration of electronic logic and memory with ever accelerating photonic and wireless communications.
Because in the ever accelerating game of 'click here to eyeball this', the battle to slay human attention spans has been fought and won.
