Graphing Position and Displacement

The motion of an object can be represented by a distance-time graph in the Figure above. In this type of graph, the y-axis represents distance and the x-axis represents time. A distance-time graph shows how far an object has traveled at any given time since it started moving. However, it doesn't show the direction(s) the object has traveled.

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Position (m)

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Unlike the distance verse time graph the displacement verse time graft can be negative.   Which means that the velocity is negative, the translation in to real world is that student is moving towards the origin.  Now if the student moves faster towards origin then the slope would be stepper.  If the student was moving away from the then the slope is positive.

For a graph of position vs. time. The slope is the rise over the run, where the rise is the displacement and the run is the time. thus,

Slope =  change in position / change in time = Average velocity

Note: Slope of the tangent line for a particular point in time = the instantaneous velocity.

For distance, as long as the object is still moving then it will be an ever increasing value so the slope will always be positive.  Position on the other hand, is allowed to have both negative and positive values which means that for certain cases the slope can be negative or positive.

Take for an example a students starts 20 meters away from the origin and walks a pace of 1 meter per second towards the origin.  If we collect data of the students position for 20 seconds we would have a table like this