You can use Media Fragments
Adding a media fragment to the media URL, you can specify the exact portion you want to play. To add a media fragment, you simply add #t=[start_time][,end_time] to the media URL. For example, to play the video between seconds 10 through 20, you could specify:
<source src="devstories.webm#t=10,20"
type='video/webm;codecs="vp8, vorbis"' />
You can also specify the times in hours:minutes:seconds, such as #t=00:01:05 to start the video at one minute, five seconds in. Or, to only play the first minute of the video, you would specify #t=,00:01:00.
You need to make sure Range Requests are supported by your server: check for Accept Ranges: bytes. It's on by default for Apache and many other servers, but worth checking.