I wanted to ask in general what area under the graph means. Also which physical quantity is highlighted by area under distance vs time graph. I'm confused that area is a 2 dimensional concept and it may indicate distance or displacement, which are 1 dimensional quantities.
Answer
The interpretation of the area under a curve, depending upon the curve, will vary. If it is a Velocity v. Time Graph, the area from a given time to another time, will be the distance traveled between those times. If it is an Acceleration v. Time Graph, the area from one time to another, will be the change in velocity of the object between those two times. For other dimensions, the quantity's significance will vary. In the case of a y v. x graph, if the unit(s)/dimension(s) of y is/are a, and the unit(s)/dimension(s) of x is/are b, then the units/dimensions of the area quantity will be 'a times b'.
For a distance v time graph, the area is indeed two dimensions, but not necessarily with both being a length. The Area under a graph is the geometrical meaning, not the physically significant one. For your situation, the area-quantity would be two dimensions: Length times Time. A quantity of this dimension is known as absement. An absement is a measure of a distance and how long something has been at that distance. Visit here for more info: https://en.wikipedia.org/wiki/Absement .
No comments:
Post a Comment