Integral of a position v time graph; meaningless?

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Homework Help Overview

The discussion revolves around the integration of a position vs. time graph and its implications, particularly focusing on the interpretation of the resulting units. Participants are exploring the relationship between different physical quantities and their representations in terms of units.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster questions the meaning of integrating a position vs. time graph, particularly regarding the resulting units. Some participants suggest that integration could be used to find average position, while others raise questions about the relevance of units like watt hours in this context.

Discussion Status

Participants are actively engaging with the concepts, with some providing insights into the relationship between units of energy and their derivations. There is a mix of interpretations being explored, particularly regarding the significance of integrating position vs. time.

Contextual Notes

There is a mention of confusion surrounding the units produced by integration and how they relate to commonly used terms in physics, such as joules and watt hours. The discussion reflects a need for clarity on these concepts without reaching a definitive conclusion.

pakmingki
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So, you have a graph of velocity vs. time. You integrate, you get position. What if you have a position vs time graph? For example, meters vs. seconds. If you integrate it, you will get meters seconds. Now, does this mean anything? For example, I've heard of "watt hours" but i simply don't understand how this makes any sense. What would it mean to integrate a position vs time graph?
 
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One reason you might want to integrate it is to find the average position.

<x>=1/T Int[x(t)dt]
 
Watt hours (more commonly seen as kilowatt hours--kwh) are a unit of energy.

Try multiplying the units for watts by the units for hours and see what you arrive with.

(J/t) * t = Joules
 
o
why not just call them joules then?
ive seen products, such as surge protectors labeled with, "handles up to 16,000 joules."
 

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