It's probably a better idea to use mysql fulltext index and use the match functions in mysql to do the searching.
http://devzone.zend.com/article/1304
It's a little more robust then what you have currently. If you want to keep it how you have, you would just need to explode and loop over the keywords to build the sql as you already suspect.
$keywords = $_POST['keyword_q'];
$keywords = explode(" ", $keywords);
$search_q = '';
foreach($keywords as $word){
$search_q .= "col1 Like '" . $word . "%' ||";
}
$search_q = substr($search_q, 0, -2); //strip off the last ||
//...