JSFiddle - React, Tailwind, and code Playground

HTML

<div id="content">
    
</div>

CSS

#content {
    height: 500px;
    overflow-y: auto;
    border: 1px solid #ddd;
    width: 150px;
    margin: 20px;
}

.newlyappend {
    height: 10px
}

JavaScript

var c = 0;
setInterval(function() {
    $('#content').append('<div class="newlyappend">Sample Text'+ c++ +'</div>');
    $('#content').scrollTop($('#content').height());
}, 1000);