When something accelerates then stops accelerating, what happens to the object?

The object continues to move in a straight line at the velocity it had when the acceleration stopped. Looking at Newton's laws of motion, you can see the acceleration and the subsequent motion covered by the 1st law. Newton's First Law: states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. * The first law here indicates that as long as there isn't an external force, the object continues to move in a straight line at an uniform velocity. This is the situation when there is no more acceleration (external force).