document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=983054>Question 983054</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An auto travels at the rate of 35-km/h, N for 6.0mins, then NE for 7.0mins and finally at 20-km/h, S for 8.0mins. what is the average velocity of the auto? Whta is the average speed of the auto? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #604007 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=604007\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It is not clearly specified,<BR>\n" );
document.write( "but it seems like after going N for 6.0 minutes at 35 km/h,<BR>\n" );
document.write( "the auto continues NE for 7.0 minutes at the same speed.<BR>\n" );
document.write( "That is what I will assume.<BR>\n" );
document.write( "The whole trip looks like this: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28200%2C400%2C-0.5%2C3.5%2C-0.5%2C7.5%2C%0D%0Acircle%280%2C0%2C0.05%29%2Ccircle%282.887%2C3.72%2C0.05%29%2C%0D%0Alocate%280.1%2C0.2%2Cstart%29%2Clocate%283%2C3.92%2Cend%29%2C%0D%0Atriangle%280%2C3.5%2C2.887%2C3.5%2C2.887%2C6.387%29%2C%0D%0Arectangle%282.887%2C3.5%2C2.737%2C3.65%29%2C%0D%0Ared%28line%280%2C0%2C0%2C3.5%29%29%2Cred%28arrow%280%2C0%2C0%2C3.5%29%29%2C%0D%0Agreen%28line%280%2C3.5%2C2.887%2C6.387%29%29%2Cgreen%28arrow%280%2C3.5%2C2.887%2C6.387%29%29%2C%0D%0Ablue%28line%282.887%2C6.387%2C2.887%2C3.72%29%29%2Cblue%28arrow%282.887%2C6.387%2C2.887%2C3.72%29%29%2C%0D%0Alocate%280.1%2C2%2Cred%28N%29%29%2Clocate%281.443%2C4.94%2Cgreen%28NE%29%29%2C%0D%0Alocate%282.9%2C5.1%2Cblue%28S%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The average velocity is a vector with magnitude and direction,<BR>\n" );
document.write( "and can be found as the start-end displacement vector divided by the travel time.<BR>\n" );
document.write( "The average speed is a scalar quantity (a number with units of km/h),<BR>\n" );
document.write( "and can be found as the total distance covered along the trajectory divided by the travel time.<BR>\n" );
document.write( "The distances traveled are as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28%22N+%3A%22%29 ALIGN=MIDDLE  ALT=\"red%28%22N+%3A%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2835km%2F%2260+minutes%22%29%2A%286minutes%29=3.5km ALIGN=MIDDLE  ALT=\"%2835km%2F%2260+minutes%22%29%2A%286minutes%29=3.5km\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28%22NE+%3A%22%29 ALIGN=MIDDLE  ALT=\"green%28%22NE+%3A%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2835km%2F%2260+minutes%22%29%2A%287minutes%29=49%2F12 ALIGN=MIDDLE  ALT=\"%2835km%2F%2260+minutes%22%29%2A%287minutes%29=49%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=km=4.083km ALIGN=MIDDLE  ALT=\"km=4.083km\"   DISABLED_style= \"max-width:90%; height:auto;\" >(rounded)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=blue%28%22S+%3A%22%29 ALIGN=MIDDLE  ALT=\"blue%28%22S+%3A%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820km%2F%2260+minutes%22%29%2A%288minutes%29=8%2F3 ALIGN=MIDDLE  ALT=\"%2820km%2F%2260+minutes%22%29%2A%288minutes%29=8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=km=2.667km ALIGN=MIDDLE  ALT=\"km=2.667km\"   DISABLED_style= \"max-width:90%; height:auto;\" >(rounded).<BR>\n" );
document.write( "Now the trips looks like this: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28250%2C400%2C-0.8%2C4.2%2C-0.5%2C7.5%2C%0D%0Acircle%280%2C0%2C0.05%29%2Ccircle%282.887%2C3.72%2C0.05%29%2C%0D%0Alocate%280.1%2C0.2%2Cstart%29%2Clocate%283%2C3.92%2Cend%29%2C%0D%0Atriangle%280%2C3.5%2C2.887%2C3.5%2C2.887%2C6.387%29%2C%0D%0Arectangle%282.887%2C3.5%2C2.737%2C3.65%29%2C%0D%0Ared%28line%280%2C0%2C0%2C3.5%29%29%2Cred%28arrow%280%2C0%2C0%2C3.5%29%29%2C%0D%0Agreen%28line%280%2C3.5%2C2.887%2C6.387%29%29%2Cgreen%28arrow%280%2C3.5%2C2.887%2C6.387%29%29%2C%0D%0Ablue%28line%282.887%2C6.387%2C2.887%2C3.72%29%29%2Cblue%28arrow%282.887%2C6.387%2C2.887%2C3.72%29%29%2C%0D%0Alocate%280.1%2C2%2Cred%283.5km%29%29%2Clocate%281.443%2C4.94%2Cgreen%284.083km%29%29%2C%0D%0Alocate%282.95%2C5.1%2Cblue%282.667km%29%29%2Clocate%281.34%2C3.5%2Cx%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The approximate total distance traveled is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.5km%2B4.083km%2B2.667km=10.250km ALIGN=MIDDLE  ALT=\"3.5km%2B4.083km%2B2.667km=10.250km\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The total travel time is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6minutes%2B7minutes%2B8minutes=21minutes ALIGN=MIDDLE  ALT=\"6minutes%2B7minutes%2B8minutes=21minutes\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The average speed of an auto that travels a total of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10.250km ALIGN=MIDDLE  ALT=\"10.250km\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21minutes ALIGN=MIDDLE  ALT=\"21minutes\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810.250km%2F%2221minutes%22%29%2860minutes%2F%221hour%22%29=29.29 ALIGN=MIDDLE  ALT=\"%2810.250km%2F%2221minutes%22%29%2860minutes%2F%221hour%22%29=29.29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22km+%2F+h%22=29 ALIGN=MIDDLE  ALT=\"%22km+%2F+h%22=29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22km+%2F+h%22 ALIGN=MIDDLE  ALT=\"%22km+%2F+h%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded).<BR>\n" );
document.write( "The eastward displacement is the horizontal leg of an isosceles right triangle with a hypotenuse of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49%2F12 ALIGN=MIDDLE  ALT=\"49%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=km=4.083km ALIGN=MIDDLE  ALT=\"km=4.083km\"   DISABLED_style= \"max-width:90%; height:auto;\" >(rounded).<BR>\n" );
document.write( "It's measure in km is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2=%2849%2F12%29%5E2=49%5E2%2F12%5E2 ALIGN=MIDDLE  ALT=\"2x%5E2=%2849%2F12%29%5E2=49%5E2%2F12%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=49%5E2%2F%282%2A12%5E2%29 ALIGN=MIDDLE  ALT=\"x%5E2=49%5E2%2F%282%2A12%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%282%2A49%5E2%2F%282%5E2%2A12%5E2%29%29=sqrt%2849%5E2%2F%282%5E2%2A12%5E2%29%29%2Asqrt%282%29=%2849%2F%282%2A12%29%29%2Asqrt%282%29=49sqrt%282%29%2F24=about2.8874 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is also the vertical leg of the same isosceles right triangle,<BR>\n" );
document.write( "which is the northward displacement during the NE portion of the trip.<BR>\n" );
document.write( "The total (approximate) northward displacement in km is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.5%2B2.887-2.667=3.72 ALIGN=MIDDLE  ALT=\"3.5%2B2.887-2.667=3.72\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Now the trips looks like this: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28250%2C400%2C-1%2C4%2C-0.5%2C7.5%2C%0D%0Acircle%280%2C0%2C0.05%29%2Ccircle%282.887%2C3.72%2C0.05%29%2C%0D%0Alocate%280.1%2C0.2%2Cstart%29%2Clocate%283%2C3.92%2Cend%29%2C%0D%0Atriangle%280%2C3.5%2C2.887%2C3.5%2C2.887%2C6.387%29%2C%0D%0Arectangle%282.887%2C3.5%2C2.737%2C3.65%29%2C%0D%0Ared%28line%280%2C0%2C0%2C3.5%29%29%2Cgreen%28line%280%2C3.5%2C2.887%2C6.387%29%29%2C%0D%0Ablue%28line%282.887%2C6.387%2C2.887%2C3.72%29%29%2C%0D%0Alocate%280.1%2C2%2Cred%283.5km%29%29%2Clocate%281.443%2C4.94%2Cgreen%284.083km%29%29%2C%0D%0Alocate%282.95%2C5.1%2Cblue%282.667km%29%29%2Clocate%280.8%2C3.5%2C2.887km%29%2C%0D%0Atriangle%280%2C0%2C2.887%2C3.72%2C0%2C3.72%29%2Crectangle%280%2C3.72%2C0.15%2C3.57%29%2C%0D%0Ared%28arc%280%2C0%2C2%2C2%2C-90%2C-52.2%29%29%2Clocate%280.2%2C0.95%2Cred%28theta%29%29%2C%0D%0Aarrow%280%2C0%2C2.887%2C3.72%29%2Clocate%281.45%2C1.86%2Cdisplacement%29%2C%0D%0Alocate%28-1%2C1.97%2C3.72km%29%2Carrow%28-0.5%2C2%2C-0.5%2C3.72%29%2Carrow%28-0.5%2C1.72%2C-0.5%2C0%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The magnitude of the displacement (in km) is approximately<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283.72%5E2%2B2.887%5E2%29=4.709 ALIGN=MIDDLE  ALT=\"sqrt%283.72%5E2%2B2.887%5E2%29=4.709\"   DISABLED_style= \"max-width:90%; height:auto;\" > .The <BR>\n" );
document.write( "The approximate) magnitude of the average velocity is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284.709km%2F%2221minutes%22%29%2860minutes%2F%221hour%22%29=13.45 ALIGN=MIDDLE  ALT=\"%284.709km%2F%2221minutes%22%29%2860minutes%2F%221hour%22%29=13.45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22km+%2F+h%22=13.5 ALIGN=MIDDLE  ALT=\"%22km+%2F+h%22=13.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22km+%2F+h%22 ALIGN=MIDDLE  ALT=\"%22km+%2F+h%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded),<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28theta%29 ALIGN=MIDDLE  ALT=\"red%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives us the direction.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28red%28theta%29%29=2.887%2F3.72=0.7761 ALIGN=MIDDLE  ALT=\"tan%28red%28theta%29%29=2.887%2F3.72=0.7761\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28theta%29=37.8%5Eo ALIGN=MIDDLE  ALT=\"red%28theta%29=37.8%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the direction is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37.8%5Eo ALIGN=MIDDLE  ALT=\"37.8%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > East of North.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );