How can we find the average speed and the average velocity from a Velocity Vs. Time graph?

And How can we find the average speed and the average velocity from a Displacement Vs. Time graph?|||Average speed = distance traveled / time, average velocity = displacement / time


To find average velocity from v vs t graph, first you want to find displacement. Displacement is the area under the velocity curve (integral v dt). The area under v but over x axis is counted as positive while the area over v but under x axis is counted as negative.


Once you get the area (or integrated), divide by the change in time.





For average speed from v vs t graph, you do the same things, except if the velocity goes negative, you still count the area over v but under x axis as positive. So you might have to divide up the integral into two parts, absolute value of integral of the negative part and the integral of the positive part. Divide by change in time again.





Average velocity from displacement vs time graph is easy. Find the difference in displacement (Df - Di) and divide by time. The difference in displacement is the same as the integral.





Average speed, from displacement, you once again may have to divide the graph up into many pieces. Every time the displacement changes from going up to down or down to up, you have to find the absolute value of the difference between the "peaks and troughs." Add up all the differences together, and divide by time.





Remember speed always has to be positive, so that is in every situation the displacement happens to be negative, you have to take the absolute value.