A straight horizontal one does.
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It means there is no movement towards or away from the point from which distances are measured - usually the origin. The object can be moving in a transverse direction at any speed and the graph would not show it.
The gradient of a distance-time graph gives the object's speed.
When there is a curved line going upwards on a graph it means the distance is increasing
Linear equation.
Object will change distance time graph when speed is changing. Distance time graph don't changed indicate of the stationary.