How to calculate instantaneous speed from a speed - time graph?
What is the definition of instantaneous speed?
If you know calculus, it should be pretty easy.
If you don't, you'll have to just use the average speed over a tiny interval of time as an approximation or learn calculus.
A method of getting (an approximation to) instantaneous speed from a graph, that I learned back in secondary school, is this: hold a small pocket mirror on the graph at the point desired and slowly turn it until the graph appears to go "smoothly" into its image in the mirrow. Hold the mirror in place there and use it as straight edge to draw a line perpendicular to the graph. Now do the same thing, rotating the mirror around that point until this new line appears to go "smoothly" into its image in the mirror. Use the mirror as a straight edge to draw the line perpendicular to this line and so tangent to the curve. Now you can extend that line as much as you need to be able to find "rise" and "run" and find the slope of that tangent line. On a "distance vs time" graph that will be the "speed" at that point.
On a speed-time graph, the instantaneous speed is the speed displayed on the graph at any point.
If you don't know calculus, you can use the method described by HallsofIvy, however the mirror won't be necessary. You just estimate the tangent line to the x-t graph (as stated by another person; speed-time graphs show the instantaneous speed at every point) and you take the slope of said tangent line.
If you do know calculus, you have to calculate the derivative of the x(t)-function, which will give you the v(t)-function.
Great answer Chestermiller !
I know, right? I was going to say this!
He must have meant x-t graph.
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