document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1078623>Question 1078623</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The braking distance of a vehicle is directly proportional to the square of its speed. when the speed of the vehicle is b m/s, its braking distance is d m. if the speed of the vehicle is increased by 200%, find the percentage increase in its braking distance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #693041 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=693041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> braking distance is directly proportional to the square of its speed.\r<BR>\n" );
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document.write( "let y = braking distance.<BR>\n" );
document.write( "let x = speed.\r<BR>\n" );
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document.write( "formula is y = kx^2\r<BR>\n" );
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document.write( "when the speed is b meters per second, the braking distance is d meters.\r<BR>\n" );
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document.write( "therefore the same formula becomes d = kb^2\r<BR>\n" );
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document.write( "k is the constant of variation and never changes once initially ste up.\r<BR>\n" );
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document.write( "if the speed of the vehicle is increased by 200%, find the percentage increase in the braking distance.\r<BR>\n" );
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document.write( "an increase in the speed of 200% means that the new speed is 3 times the original speed.\r<BR>\n" );
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document.write( "therefore, the formula for d becomes d = k*(3b)^2\r<BR>\n" );
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document.write( "simplify this to get d = k*9b^2\r<BR>\n" );
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document.write( "therefore, the ratio of the new distance divided by the old distance is k * 9b^2 / k * b^2\r<BR>\n" );
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document.write( "simplify to get the ratio of the new distance to the old distance is 9/1\r<BR>\n" );
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document.write( "this means that the increase in the distance is 800% because 9/1 - 1/1 = 8/1 = 800%.\r<BR>\n" );
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document.write( "to see if this works, let's try an arbitrary example.\r<BR>\n" );
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document.write( "assume the car is traveling at 30 meters per second.\r<BR>\n" );
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document.write( "assume it takes the car 1200 meters to stop when it is traveling at 30 miles per hour.\r<BR>\n" );
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document.write( "d = k * b^2 becomes 1200 = k * 900\r<BR>\n" );
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document.write( "solve for k to get k = 1200/900 = 12/9 = 4/3\r<BR>\n" );
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document.write( "k is the constant of variation.\r<BR>\n" );
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document.write( "now assume the speed is increased by 200%.\r<BR>\n" );
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document.write( "that means it's increased by 60 meters per second.\r<BR>\n" );
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document.write( "that means the car is traveling 90 meters per second.\r<BR>\n" );
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document.write( "the formula becomes d = 4/3 * 90^2\r<BR>\n" );
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document.write( "this gets you d = 10800 meters.\r<BR>\n" );
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document.write( "it originally took 1200 meters to stop at 30 meters per second and now it takes 10800 meters at 90 meters per second.\r<BR>\n" );
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document.write( "10800 - 1200 equals an increase of 9600 meters.\r<BR>\n" );
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document.write( "9600 / 1200 = an increase of 8 times which is an increase of 800%.\r<BR>\n" );
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document.write( "looks like the formula works.\r<BR>\n" );
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document.write( "an increase of 200% in the speed results in an increase of 800% in the stopping distance.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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