document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148805>Question 148805</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Pls. help me with this. There are so many given I don't know what to do with all of it or what to use.\r<BR>\n" );
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document.write( "A drag racer accelerates uniformly from rest straight track at 12m/s^2 for 5.5s, maintains the speed it has reached for 3.0s, and slows down to a stop at the rate of -14m/s^2. What is the total distance traveled by the racer? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109135 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=109135\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The easiest way to approach this is to look at it as three steps of a bigger problem.\r<BR>\n" );
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document.write( "The general formula that relates distance to acceleration and speed is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bt%5D=+%28a%2F2%29t%5E2+%2B+v%5B0%5Dt+%2B+d%5B0%5D ALIGN=MIDDLE  ALT=\"d%5Bt%5D=+%28a%2F2%29t%5E2+%2B+v%5B0%5Dt+%2B+d%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > where a is acceleration, v[0] is initial velocity and d[0] is initial position. \r<BR>\n" );
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document.write( "It is also helpful to know that velocity is related to acceleration as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5Bt%5D+=+at+%2B+v%5B0%5D ALIGN=MIDDLE  ALT=\"v%5Bt%5D+=+at+%2B+v%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So let's do this problem in three pieces.\r<BR>\n" );
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document.write( "1 - A drag racer accelerates uniformly from rest straight track at 12m/s^2 for 5.5s.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bt%5D+=+%28a%2F2%29t%5E2+%2B+v%5B0%5Dt+%2B+d%5B0%5D ALIGN=MIDDLE  ALT=\"d%5Bt%5D+=+%28a%2F2%29t%5E2+%2B+v%5B0%5Dt+%2B+d%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B5.5%5D+=+6%285.5%29%5E2+%2B+0%2A5.5+%2B+0+ ALIGN=MIDDLE  ALT=\"d%5B5.5%5D+=+6%285.5%29%5E2+%2B+0%2A5.5+%2B+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B5.5%5D+=+181.5+m ALIGN=MIDDLE  ALT=\"d%5B5.5%5D+=+181.5+m\"   DISABLED_style= \"max-width:90%; height:auto;\" >  This problem is nice because the units do not require any conversion (you are given acceleration in m/s^2 and time in seconds)\r<BR>\n" );
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document.write( "Let's find our speed at the end of 5.5 seconds<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5Bt%5D+=+at+%2B+v%5B0%5D ALIGN=MIDDLE  ALT=\"v%5Bt%5D+=+at+%2B+v%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B5.5%5D+=+12%2A5+%2B+0+ ALIGN=MIDDLE  ALT=\"v%5B5.5%5D+=+12%2A5+%2B+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B5.5%5D+=+60m%2Fs ALIGN=MIDDLE  ALT=\"v%5B5.5%5D+=+60m%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So at the end of the first leg, we have moved 181.5m and are zipping along at 60m/s\r<BR>\n" );
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document.write( "Now let's do the second leg as a 'whole new problem'.<BR>\n" );
document.write( "maintains the speed it has reached for 3.0s<BR>\n" );
document.write( "In this leg, the acceleration is 0 and the initial speed is where ended up at the end of the first leg - 60m.s<BR>\n" );
document.write( "For this leg, we'll start our clock over again at 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bt%5D=+%28a%2F2%29t%5E2+%2B+v%5B0%5Dt+%2B+d%5B0%5D ALIGN=MIDDLE  ALT=\"d%5Bt%5D=+%28a%2F2%29t%5E2+%2B+v%5B0%5Dt+%2B+d%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B3%5D+=+0%2A3%5E2+%2B+60%2A3+%2B+0%2At ALIGN=MIDDLE  ALT=\"d%5B3%5D+=+0%2A3%5E2+%2B+60%2A3+%2B+0%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B3%5D+=+0+%2B+180+%2B+0+ ALIGN=MIDDLE  ALT=\"d%5B3%5D+=+0+%2B+180+%2B+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B3%5D+=+180m ALIGN=MIDDLE  ALT=\"d%5B3%5D+=+180m\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, we could have gotten more complicated and setup the equation to use to use the same clock as first leg, but that requires getting a lot more complex about where we are, what time it is, etc. More trouble than it is worth. \r<BR>\n" );
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document.write( "For now, just remember that we broke this problem into three small parts. And we will need to put humpty back together again in order to get a 'final answer'.\r<BR>\n" );
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document.write( "Ok, so we are at the end of the second leg. Let's see where we are now and see how fast we are going.\r<BR>\n" );
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document.write( "Our position is the sum of the first two legs. Our time is the sum of the first two leg's times.<BR>\n" );
document.write( "Time at the end of the second leg is 5.5+3 = 8.5 seconds<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B8.5%5D+=+distanceLeg1+%2B+distanceLeg2 ALIGN=MIDDLE  ALT=\"d%5B8.5%5D+=+distanceLeg1+%2B+distanceLeg2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B8.5%5D+=+181.5+%2B+180 ALIGN=MIDDLE  ALT=\"d%5B8.5%5D+=+181.5+%2B+180\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B8.5%5D+=+361.5m ALIGN=MIDDLE  ALT=\"d%5B8.5%5D+=+361.5m\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we are ready for the last leg. At the end of 8.5 seconds, we are still going 60m/s since we did not change speeds on the second leg. We are 361 meters down the road.\r<BR>\n" );
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document.write( "Now we are told to -- slow down to a stop at the rate of -14m/s^2.<BR>\n" );
document.write( "Again, let's treat this as a small standalone problem. <BR>\n" );
document.write( "First, we need to figure out how long it takes to stop. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5Bt%5D+=+at+%2B+v%5B0%5D ALIGN=MIDDLE  ALT=\"v%5Bt%5D+=+at+%2B+v%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-14t+%2B+60 ALIGN=MIDDLE  ALT=\"0+=+-14t+%2B+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-60%2F-14+=+t ALIGN=MIDDLE  ALT=\"-60%2F-14+=+t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F7+=+t ALIGN=MIDDLE  ALT=\"30%2F7+=+t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So it takes about 4.3 seconds to stop.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bt%5D+=+%28a%2F2%29t%5E2+%2B+v%5B0%5Dt+%2B+d%5B0%5D ALIGN=MIDDLE  ALT=\"d%5Bt%5D+=+%28a%2F2%29t%5E2+%2B+v%5B0%5Dt+%2B+d%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B4.3%5D+=+-7%284.3%29%5E2+%2B+60%2A4.3+%2B+0 ALIGN=MIDDLE  ALT=\"d%5B4.3%5D+=+-7%284.3%29%5E2+%2B+60%2A4.3+%2B+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B4.3%5D+=+-129.43+%2B+258 ALIGN=MIDDLE  ALT=\"d%5B4.3%5D+=+-129.43+%2B+258\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B4.3%5D+=+128.57m ALIGN=MIDDLE  ALT=\"d%5B4.3%5D+=+128.57m\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So add in the distance from the last leg to the total so far to get:<BR>\n" );
document.write( "TotalDistance = 361.5 + 128.57<BR>\n" );
document.write( "TotalDistance is approximately 490m\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );