Writing Question (Position-Time Graph)

ihatephysics

How can you find average velocity from a position-time graph? How can you find instantaneous velocity from a position-time graph?

Any help is appreciated!

kreil

The velocity on a position-time graph is equal to the slope, so the average velocity is equal to the average slope.

The instantantaneous velocity on a position-time graph can be found by finding the slope of the line tangent to the graph at the instance of time in question.

HallsofIvy

A little expansion on kreil's post: Choose two points on the graph. Subtract the "x-coordinates" (change in position), subtract the "t-coordinates" (change in time) and divide the first by the second,
[tex]\frac{\Delta x}{\Delta t}[/itex]
is the slope of the line and the average velocity. To find the instantaneous velocity, find the slope of the tangent line. Finding the tangent line itself is harder (and is why Newton and Leibniz get so much press!). When I was in school, we did this: take a small mirror and put it across the graph at the point at which you want to find the tangent line. Turn the mirror on that point until the graph seems to flow smoothly into its image (no "corner"). Use the mirror as a straightedge to draw a line there. That line is perpendicular to the curve. Now do the same to draw a line perpendicular to the perpendicular. That line will be the tangent line.