document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=697502>Question 697502</A>: <I><SPAN STYLE=\"word-break: break-all;\"> kinematic question:a highway patrol at rest is passed by a bus travelling at constant speed of 126 km/h.two seconds later the patrol car starts accelerates at a constant rate of 5m/s2 until it reaches a speed of 162 km/h.if the patrol car then maintains a constant speed of 162km/h , determine the distance travelled by the patrol car to overtake the bus.\r<BR>\n" );
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document.write( "thank you tutor. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #430932 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=430932\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I suspect you are taking physics in high school or college.<BR>\n" );
document.write( "However, to cover any possible situation, I'll add the physics \"formulas\" in parenthesis,<BR>\n" );
document.write( "but I will show the solution as if it was a problem for a fifth grader.<BR>\n" );
document.write( "A physics instructor may expect a different way to solve the problem,<BR>\n" );
document.write( "but I hope I found the simplest way,<BR>\n" );
document.write( "and I believe the simplest way is the best way.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Some painful conversions seem needed,<BR>\n" );
document.write( "but the numbers were chosen so as to make this easier.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=126km%2F1hr=126%2A1000m%2F3600s=35 ALIGN=MIDDLE  ALT=\"126km%2F1hr=126%2A1000m%2F3600s=35\"   DISABLED_style= \"max-width:90%; height:auto;\" >m/s<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=162km%2F1hr=162%2A1000m%2F3600s=45 ALIGN=MIDDLE  ALT=\"162km%2F1hr=162%2A1000m%2F3600s=45\"   DISABLED_style= \"max-width:90%; height:auto;\" >m/s<BR>\n" );
document.write( " <BR>\n" );
document.write( "Accelerating from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45 ALIGN=MIDDLE  ALT=\"45\"   DISABLED_style= \"max-width:90%; height:auto;\" >m/s at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >m/s of speed increase per second takes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2F5=9 ALIGN=MIDDLE  ALT=\"45%2F5=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds.<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v-v%5B0%5D=a%2At ALIGN=MIDDLE  ALT=\"v-v%5B0%5D=a%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28v-v%5B0%5D%29%2Fa ALIGN=MIDDLE  ALT=\"t=%28v-v%5B0%5D%29%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > but for this case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B0%5D=0 ALIGN=MIDDLE  ALT=\"v%5B0%5D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "While accelerating, the police car has an average speed of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2845%2B0%29%2F2=22.5 ALIGN=MIDDLE  ALT=\"%2845%2B0%29%2F2=22.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >m/s<BR>\n" );
document.write( "(because at constant acceleration, the average velocity is the average of the initial and final velocities)<BR>\n" );
document.write( "so in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" >s it covers a distance of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2A22.5=202.5 ALIGN=MIDDLE  ALT=\"9%2A22.5=202.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >m<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=v%2At ALIGN=MIDDLE  ALT=\"d=v%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( " <BR>\n" );
document.write( "The distance (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >, in meters) covered by the bus and also by the police car can be calculated from either point of view.<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=v%2At ALIGN=MIDDLE  ALT=\"d=v%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "The bus is moving for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35 ALIGN=MIDDLE  ALT=\"35\"   DISABLED_style= \"max-width:90%; height:auto;\" >m/s, covering a distance of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=35%2At ALIGN=MIDDLE  ALT=\"d=35%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" > meters.<BR>\n" );
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document.write( "During those <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds, the police car is stopped for 2 seconds,<BR>\n" );
document.write( "covers <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=202.5 ALIGN=MIDDLE  ALT=\"202.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >m for the next <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds (while accelerating),<BR>\n" );
document.write( "and after those  first <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds,<BR>\n" );
document.write( "moves at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45 ALIGN=MIDDLE  ALT=\"45\"   DISABLED_style= \"max-width:90%; height:auto;\" >m/s for the rest of the time (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t-11 ALIGN=MIDDLE  ALT=\"t-11\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds).<BR>\n" );
document.write( "The distance covered by the police car is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=202.5%2B45%28t-11%29=202.5%2B45t-495=45t-292.5 ALIGN=MIDDLE  ALT=\"202.5%2B45%28t-11%29=202.5%2B45t-495=45t-292.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > meters<BR>\n" );
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document.write( "Because the same distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > is covered by the bus and by the car<BR>\n" );
document.write( "during the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds between the time the bus passes the patrol car and the time the patrol car overtakes the bus.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45t-292.5=35t ALIGN=MIDDLE  ALT=\"45t-292.5=35t\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45t-35t=292.5 ALIGN=MIDDLE  ALT=\"45t-35t=292.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10t=292.5 ALIGN=MIDDLE  ALT=\"10t=292.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=292.5%2F10 ALIGN=MIDDLE  ALT=\"t=292.5%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t=29.25%29 ALIGN=MIDDLE  ALT=\"highlight%28t=29.25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Substituting into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=35t ALIGN=MIDDLE  ALT=\"d=35t\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=35%2A29.25 ALIGN=MIDDLE  ALT=\"d=35%2A29.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28d=1023.75%29 ALIGN=MIDDLE  ALT=\"highlight%28d=1023.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > meters (about 1 km). </SPAN>\n" );
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