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The slope of a  position-time graph at any given instant in time or during any given time interval is equal to the velocity of the object at that time or during that time interval. Being a vector, velocity has a direction. For graphs, that direction is often associated with the positive and negative sign on the slope.

 

There are four nearly identical versions of this question. Each version involves a slope calculation for an upward-sloped line. Two of the versions are shown below.

Version 1
This position-time graph describes an object's motion. Use it to determine the velocity (in m/s) of the object. Enter the appropriate + or – sign.

 
 
Version 2
This position-time graph describes an object's motion. Use it to determine the velocity (in m/s) of the object. Enter the appropriate + or – sign.


 

The slope of the line on a position-time graph is the velocity. So this question involves calculating slope. To do so, you will need to determine the "x, y" coordinates of two points on the line. Pick points for which you are certain of what the coordinates are. The point (0 s, 0 m) would be a good choice since it is on the line. The last point on the graph is also a good choice. Once you've selected the two points, calculate the ratio of the y-coordinate difference divided by the x-coordinate difference. That is, determine the ratio of ∆position to ∆time.

Sometimes the above procedure is called the rise per run method. That is what slope means - by how much does the line rise upward for every 1 unit of run across the horizontal axis. If you determine a slope of the line to be +4 m/s, then you have determined that for every 1 second of motion, the object changes its position by 4 meters. The process of determining this slope always involves finding the change in the vertical coordinate divided by the change in the horizontal coordinate for any two points located on the line.
 


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