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The speed of an object is given as the ratio of distance traveled to time taken. That is,
Speed = distance/time
Therefore, the greater the slope of the position-time plot, higher will be the speed.
The distance can be computed as change in position (from location x1 to location x2) in time duration ( from t1 to t2). Using these variables, the speed can be calculated as:
Speed = (x2 - x1)/ (t2 - t1)
Thus equation is similar to slope intercept form of equation of line, except that intercept is 0 here. Using this knowledge, we can calculate the speed as the slope of position-time graph. The greater the slope of the position-time plot, higher will be the speed. Similarly, lower or gentler slope refers to less distance covered in given time and hence equates to lesser speed of the object.
Hence, given the locations of an object as a function of time, we can calculate the speed of the object.
Hope this helps.
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