submit the form using ajax

Nobody has actually given a pure javascript answer (as requested by OP), so here it is:

function postAsync(url2get, sendstr)    {
    var req;
    if (window.XMLHttpRequest) {
        req = new XMLHttpRequest();
        } else if (window.ActiveXObject) {
        req = new ActiveXObject("Microsoft.XMLHTTP");
        }
    if (req != undefined) {
        // req.overrideMimeType("application/json"); // if request result is JSON
        try {
            req.open("POST", url2get, false); // 3rd param is whether "async"
            }
        catch(err) {
            alert("couldnt complete request. Is JS enabled for that domain?\\n\\n" + err.message);
            return false;
            }
        req.send(sendstr); // param string only used for POST

        if (req.readyState == 4) { // only if req is "loaded"
            if (req.status == 200)  // only if "OK"
                { return req.responseText ; }
            else    { return "XHR error: " + req.status +" "+req.statusText; }
            }
        }
    alert("req for getAsync is undefined");
}

var var_str = "var1=" + var1  + "&var2=" + var2;
var ret = postAsync(url, var_str) ;
    // hint: encodeURIComponent()

if (ret.match(/^XHR error/)) {
    console.log(ret);
    return;
    }

In your case:

var var_str = "video_time=" + document.getElementById('video_time').value 
     + "&video_id=" + document.getElementById('video_id').value;