I presume this means you don't get videos breaking up. You are lucky. I sometimes have to give up watching a short news report or YouTube vid if I can't watch 5 seconds at a stretch.
That's got nothing really to do with the speed of your broadband. The 1.9Mbps you say you're getting is easily enough for realtime streaming video as that usually has a maximum bitrate of about 512kbps.
It can, however, be caused by many other problems such as contention at the DSLAM in the exchange, poor/busy network infrastructure at the exchange, slow/congested/faulty/problematic link(s) somewhere between the exchange and the source of the video stream, or routing problems sending some packets a longer/slower route between the two.
As for avoiding it, just hit pause on the video stream and do something else for 30 seconds or longer whilst it continues to load. When you come back to the page it will have buffered a lot more of the stream and you should avoid seeing it break up as it runs out of buffered data.