What Does the Area Under a Position vs. Time Graph Represent?

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The area under a position vs. time graph does not have a meaningful physical interpretation, as it results in units of length multiplied by time, which lacks significance. In contrast, the area under a velocity vs. time graph represents total displacement or total distance traveled when considering absolute values. This distinction highlights the difference in the implications of these two types of graphs in physics. Overall, the area under a position vs. time graph is not considered to convey useful information. Understanding these relationships is crucial for interpreting motion graphs accurately.
Rock32
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This isn't really a homework problem, but I wasn't sure where else to ask this.

The area under (integral) a velocity vs. time graph is total displacement, or if it is absolute value'd, total distance traveled. So then, what does the area under a position vs. time graph signify, if anything?

Thanks
 
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I don't think it signifies anything. The area under a velocity vs time curve has units length/time unit x time, giving you length. The area under a position vs. time curve has units length x time, which doesn't have any significance that I know about.
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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