how to convert date in excel to sql format using php?

The value store in PHPExcel is an Excel serialized datetime value (a float, representing the number of days since 1/1/1900 or 1/1/9004 depending on whether Windows or Mac Calendar was used). You need to convert this to a Unix timestamp or a PHP DateTime object to use PHP date functions against it for setting the format

Taken directly from the PHPExcel Date handling code:

function ExcelToPHP($dateValue = 0, $ExcelBaseDate = 1900) {
    if ($ExcelBaseDate == 1900) {
        $myExcelBaseDate = 25569;
        //    Adjust for the spurious 29-Feb-1900 (Day 60)
        if ($dateValue < 60) {
            --$myExcelBaseDate;
        }
    } else {
        $myExcelBaseDate = 24107;
    }

    // Perform conversion
    if ($dateValue >= 1) {
        $utcDays = $dateValue - $myExcelBaseDate;
        $returnValue = round($utcDays * 86400);
        if (($returnValue <= PHP_INT_MAX) && ($returnValue >= -PHP_INT_MAX)) {
            $returnValue = (integer) $returnValue;
        }
    } else {
        $hours = round($dateValue * 24);
        $mins = round($dateValue * 1440) - round($hours * 60);
        $secs = round($dateValue * 86400) - round($hours * 3600) - round($mins * 60);
        $returnValue = (integer) gmmktime($hours, $mins, $secs);
    }

    // Return
    return $returnValue;
}    //    function ExcelToPHP()

Set $ExcelBaseDate to 1900 or 1904 as necessary to indicate the Excel base calendar that you're using: Windows 1900 or Mac 1904

and if you want a PHP DateTime object instead:

function ExcelToPHPObject($dateValue = 0) {
    $dateTime = ExcelToPHP($dateValue);
    $days = floor($dateTime / 86400);
    $time = round((($dateTime / 86400) - $days) * 86400);
    $hours = round($time / 3600);
    $minutes = round($time / 60) - ($hours * 60);
    $seconds = round($time) - ($hours * 3600) - ($minutes * 60);

    $dateObj = date_create('1-Jan-1970+'.$days.' days');
    $dateObj->setTime($hours,$minutes,$seconds);

    return $dateObj;
}    //    function ExcelToPHPObject()

try

$date = str_replace('/', '-', $cell);
$start_date = date('Y-m-d', strtotime($date));

You can skip doing this, and ask MySQL to read whatever date format you have to its own DateTime type. Use STR_TO_DATE(yourdatefield, '%d/%m/%Y') in MySQL and optionally change the last argument to fit your needs... The last argument tells MySQL in what format to expect the date string.