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I'm given the following information:

\begin{array}{|l|l|l|l|l|l|l|l|} \hline t & 0 & 0.5 & 1.0 & 1.5 & 2.0 & 2.5 & 3.0 \\ v(t) & 3.4 & 4.7 & 6.3 & 8.5 & 9.3 & 9.9 & 10.2 \\ \hline \end{array}

The table represents the velocity of a moving object at time t after passing a particular position.

I'm supposed to find how far the object moves from 0 to 3 seconds. Is this the correct way to do it?

$ \frac{3 - 0}{7} \cdot (3.4 + 4.7 + 6.3 + 8.5 + 9.3 + 9.9 + 10.2 ) $

Leaving me with the answer of: 22.41

EDIT

Left Hand Side:

$ \frac{1}{2}(3.4 + 4.7 + 6.3 + 8.5 + 9.3 + 9.9) $

21.05

Right Hand Side:

$ \frac{1}{2}(4.7 + 6.3 + 8.5 +9.3 +9.9 +10.2) $

24.45

Average:

22.75

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    @mi$x$edmath Thank you, that is exactly what I was trying to do.2012-12-10

1 Answers 1

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You can't determine how far the object moves because you don't know its velocity except at isolated points. You can get an estimate of how far it may have moved if its velocity didn't change too abruptly, by applying the trapezoidal rule. This would involve replacing the denominator $7$ by $6$ and weighting the first and last velocity values by $1/2$.

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    I will definitely look into it (as I'll be taking Calc II in the near future and from what I hear it goes into greater depths dealing with area). I was just wanting to make sure I understand the general idea of it prior to my test :) Thanks for the help!2012-12-10