I've tried using the autoplay tag, and .load() .play() still need to be called at least in chrome (maybe its my settings).
the simplest cross browser way to do this with jquery using your example would be
var $video = $('#divVideo video'),
videoSrc = $('source', $video).attr('src', videoFile);
$video[0].load();
$video[0].play();
However the way I'd suggest you do it (for legibility and simplicity) is
var video = $('#divVideo video')[0];
video.src = videoFile;
video.load();
video.play();
Further Reading http://msdn.microsoft.com/en-us/library/ie/hh924823(v=vs.85).aspx#ManagingPlaybackInJavascript
Additional info: .load() only works if there is an html source element inside the video element (i.e. <source src="demo.mp4" type="video/mp4" />)
The non jquery way would be:
HTML
<div id="divVideo">
<video id="videoID" controls>
<source src="test1.mp4" type="video/mp4" />
</video>
</div>
JS
var video = document.getElementById('videoID');
video.src = videoFile;
video.load();
video.play();