WITHOUT USING JAVASCRIPT
Just add #t=[(start_time), (end_time)]
to the end of your media URL. The only setback (if you want to see it that way) is you'll need to know how long your video is to indicate the end time.
Example:
<video>
<source src="splash.mp4#t=10,20" type="video/mp4">
</video>
Notes: Not supported in IE