Adistance-time graph shows a horizontal line at a distance of 3 km. explain the motion of the object.

On a distance/time graph, a horizontal line says that the distance isn't changing as time goes on.  

That means the object isn't moving.  It is, as they say, "at rest" .

Distance is constant when a graph shows a horizontal line at a distance of 3 km.

Explanation:

A distance time graph is used to denote that the relation between the distance and time as the object moves. In the graph, distance is marked on the Y axis, and time is marked on the X axis.

A linear line of the graph will indicate that the time increases as the distance also increases which is also an indication of linear velocity. A horizontal line of the graph illustrates that the distance is constant as the time increases when the object is at 3 km.