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Definition: Instantaneous velocity is defined mathematically:
Find the runner's instantaneous velocity at t = 1.00 s. As a first estimate, find the average velocity for the total observed part of the run. We have,
|= = = 4 m/s.||(3)|
|= = = 2 m/s.||(4)|
We can interpret the instantaneous velocity graphically as follows. Recall that the average velocity is the slope of the line joining P and Q (from Figure 2.1). To get the instantaneous velocity we need to take t 0, or P Q. When P Q, the line joining P and Q approaches the tangent to the curve at P (or Q). Thus the slope of the tangent at P is the instantaneous velocity at P. Note that if the trajectory were a straight line, we would get v = , the same for all t .