When time is taken on X-axis and distance is taken on Y-axis , the distance –time graph of an object at rest is
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at rest
The body does not move as the body is at same position at all times.
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position-time and displacement-time are exactly the same thing - though you could be using a slightly different definition.
A displacement time graph simply shows where an object is at a given time. Consider a train on tracks - let's let 'X' be the distance from the end of the tracks. As the train leaves the station, X increases. The rate of increase depends solely on how fast it is going (steeper=faster).
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