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I'm doing some very basic physics tasks and something that seems to come up a lot is the following. Being able to view when(seconds) the speed (m/s) is equal to some average-speed calculated in an earlier step. The graph would have seconds on the x-axis and distance/meters on the y-axis. So the derivative of this would be a function of speed by time. v(t). The graph is s(t). Quite simple if the expression is given because then I would just find the derivative and solve for when v(t) would be equal to this average speed. But on these tasks I only have the average over some time calculated delta y over delta x style. Is there some trick to find this, not 100% accurately, from just looking at the graph? Due to the wording in the tasks I don't think an exact answer is required, because the answers in the back is given like around about 4 secs. etc.

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up vote 2 down vote accepted

Given the graph you describe, the average speed is represented by the slope of a certain line connecting two separated points on the curve. (Such a line is called a secant line). The instantaneous velocity is represented by the slope of a tangent line. So graphically, I would draw in the relevant secant line and look for a point (there may be more than one) on the curve where the tangent line is parallel to that secant line. Its $x$-coordinate is the time when instantaneous velocity equals the average velocity that has been specified. Of course, since this all depends on your sketching and eyeballing skills, you aren't guaranteed to get the answer "exactly right", but it sounds like you will be close enough.

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This! Thank you. That didn't occur to me. – Algific Jan 29 '12 at 22:07

Well yes, pick a point, draw the tangent line, calculate delta y over delta x style

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