Steps to reproduce: Build a long track of rails, place one powered rail at one end and the next one many blocks away, until the minecart barely reaches it after being moved by the first powered rail. If the minecart is really slow (multiple seconds per meter) when it reaches the rail, it doesn't get sped up. The rail just works as a regular rail.
I currently can't attach a video, because my PC doesn't work and I'm playing on my laptop (too slow). If someone can reproduce it and make a video, that would be great.