document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=466628>Question 466628</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A car drives down a road in such a way that its velocity ( in m/s) at time t (seconds) is\r<BR>\n" );
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document.write( "v(t)=2(t)^1/2+4\r<BR>\n" );
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document.write( "Find the car's average velocity (in m/s) between t=4 and t=7.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #319926 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=319926\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have to find the average value of the velocity, so we integrate v(t) from t = 4 to t = 7, then divide by 3 seconds. This is similar to finding the total distance traveled, then dividing by 3 s to find the average velocity.\r<BR>\n" );
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document.write( "Integrating,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \int_{4}^{7} 2t^{\frac{1}{2}} + 4\, dt = \frac{4}{3}t^{\frac{3}{2}} + 4t \">\r<BR>\n" );
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document.write( "Evaluate it at t = 7, subtract the value at t = 4:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (\frac{4}{3}7^{\frac{3}{2}} + 4(7)) - (\frac{4}{3}4^{\frac{3}{2}} + 4(3)) = \frac{4}{3} + \frac{28\sqrt{7}}{3}\"> (meters)\r<BR>\n" );
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document.write( "Divide by 3 seconds to obtain\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{4}{9} + \frac{28\sqrt{7}}{9}\"> (meters per second) </SPAN>\n" );
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