<p>jschopen:</p>
<p>You are solving for distance, which is the integral of the absolute value of velocity.</p>
<p>How do I know which of these equations I should use? Usually these questions ask for the average value or average rate of change. </p>
<p>(1/b-a) integral from a to b of f(x)</p>
<p>f(b)-f(a)/b-a</p>
<p>INT(a to b) f(x)dx = f(b) - f(a), so they’re the same thing (you probably knew that, though).</p>
<p>If you can easily figure out (or already know) exactly what f(b) and f(a) are, then use the bottom one.
If you’re given a messy function and have a calculator, use the top one.</p>
<p>Also, for piece-wise graphs (or any graph, for that matter), don’t forget to realize that the average value equals (total area of graph) / (b-a)</p>
<p>Thank you jared</p>
<p>jschopen:</p>
<p>You’re welcome</p>
<p>ChemE14:</p>
<p>That helps, but if they are asking for the average velocity from t=0 to 3 of v(t) I would use the top function? Would I ever use the bottom function for this type of problem?</p>
<p>Wait… I messed up a little, sort of. Darn.</p>
<p>For the average value of a function ‘f’, you can use either</p>
<p>[INT(from a to b) f(x)dx] / (b-a)</p>
<p>OR</p>
<p>[F(b) - F(a)] / (b-a), where F is the antiderivative of f.</p>
<p>So if you’re given the velocity function, the v(t) function is essentially the f(x) function above, so you want to integrate it and divide by b-a. (Remember, average velocity also equals [s(b) - s(a)] / b-a, where s(t) is the position function)</p>
<p>If you did [v(3) - v(0)] / (3 - 0), that would get you average acceleration.</p>
<p>You can always do a “units check” if you’re unsure. If you did [v(3) - v(0)] / (3-0), realize that this answer’s units is (are? who needs grammar) m/s^2, since the numerator has units of “m/s” and the denominator has units of “s”.</p>
<p>Edit: Note to ryanxing - I (hopefully) answered your question on the previous page, in case you missed it. Also hope you see it before the test tomorrow!</p>
<p>Thanks ChemE14, that clarified the concept for me.</p>
<p>What are the calculator functions we need to know? Can someone please give a quick summary of the functions and how to do it on our calculators?</p>
<p>Here some major things:</p>
<p>1) Graph/view functions</p>
<p>2) Take derivative at a point.</p>
<p>3) Calculate a definite integral.</p>
<p>4) Find intersections/solve functions</p>