document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1092443>Question 1092443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the stopping distances for a car with an initial speed of 93 km/h and human reaction time of 3.0 s for the following accelerations.<BR>\n" );
document.write( "(a) a = -4.0 m/s^2\r<BR>\n" );
document.write( "\n" );
document.write( "(b) a = -8.0 m/s^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #707131 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=707131\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> IN IDEAS:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2293+km+%2F+h%22=93%2A1000%2F3600 ALIGN=MIDDLE  ALT=\"%2293+km+%2F+h%22=93%2A1000%2F3600\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22m+%2F+s%22=93%2F3.6 ALIGN=MIDDLE  ALT=\"%22m+%2F+s%22=93%2F3.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22m+%2F+s+%22=%22about+25.833+m+%2F+s%22 ALIGN=MIDDLE  ALT=\"%22m+%2F+s+%22=%22about+25.833+m+%2F+s%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "At that speed, during the 3.0 seconds allowed for reaction time,<BR>\n" );
document.write( "the vehicle would cover a distance of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=93%2F3.6 ALIGN=MIDDLE  ALT=\"93%2F3.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22m+%2F+s%22%2A%223.0+s%22=77.5m ALIGN=MIDDLE  ALT=\"%22m+%2F+s%22%2A%223.0+s%22=77.5m\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The graph of speed (in m/s) as a function of time (in seconds)<BR>\n" );
document.write( "for the first case (a=-4.0m/s^2) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C300%2C-2%2C8%2C-3%2C27%2Cgrid%280%29%2C%0D%0Aline%280%2C25.83%2C3%2C25.83%29%2Cline%283%2C25.83%2C6.458%2C0%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the stopping distance is the area under the curve.<BR>\n" );
document.write( "To go from initial speedspeed to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%220+m+%2F+s%22 ALIGN=MIDDLE  ALT=\"%220+m+%2F+s%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%22-4.0%22 ALIGN=MIDDLE  ALT=\"a=%22-4.0%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2Fs%5E2 ALIGN=MIDDLE  ALT=\"m%2Fs%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > it would take <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2893%2F3.6%29%29%2F4.0 ALIGN=MIDDLE  ALT=\"%28%2893%2F3.6%29%29%2F4.0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=93%2F14.4 ALIGN=MIDDLE  ALT=\"s=93%2F14.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s ALIGN=MIDDLE  ALT=\"s\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "During that time, speed would be changing linearly,<BR>\n" );
document.write( "with an average speed of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2893%2F3.6%2B0%29%2F2 ALIGN=MIDDLE  ALT=\"%2893%2F3.6%2B0%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22m+%2F+s%22=93%2F7.2 ALIGN=MIDDLE  ALT=\"%22m+%2F+s%22=93%2F7.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22m+%2F+s%22=%22about12.917+m+%2F+s%22 ALIGN=MIDDLE  ALT=\"%22m+%2F+s%22=%22about12.917+m+%2F+s%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and covering a distance of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2893%2F14.4%29%2A%2893%2F7.2%29 ALIGN=MIDDLE  ALT=\"%2893%2F14.4%29%2A%2893%2F7.2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%22about+83.42+m%22 ALIGN=MIDDLE  ALT=\"m=%22about+83.42+m%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The total stopping distance would be about<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=77.5m%2B83.42m=160.92m ALIGN=MIDDLE  ALT=\"77.5m%2B83.42m=160.92m\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As the acceleration and initial speed were given with two significant digits,<BR>\n" );
document.write( "it would be proper to report the stopping distance as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28161%29m ALIGN=MIDDLE  ALT=\"highlight%28161%29m\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "With an acceleration of -8.0 m/s^2 (twice as large in magnitude),<BR>\n" );
document.write( "the stopping time would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=93%2F38.8 ALIGN=MIDDLE  ALT=\"93%2F38.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=%22about+3.229+s%22 ALIGN=MIDDLE  ALT=\"s=%22about+3.229+s%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "During that time, with the same average speed calculated above,<BR>\n" );
document.write( "the vehicle would cover a distance of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2893%2F14.4%29%2A%2893%2F38.8%29 ALIGN=MIDDLE  ALT=\"%2893%2F14.4%29%2A%2893%2F38.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%22about+41.71+m%22 ALIGN=MIDDLE  ALT=\"m=%22about+41.71+m%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That results in a total stooping distance of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=77.5m%2B41.72m=119.2m ALIGN=MIDDLE  ALT=\"77.5m%2B41.72m=119.2m\"   DISABLED_style= \"max-width:90%; height:auto;\" > to be reported as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28119m%29 ALIGN=MIDDLE  ALT=\"highlight%28119m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "IN FORMULAS:<BR>\n" );
document.write( "With d=distance, v=velocity, a=acceleration, and t=time, in SI units (only meters and seconds allowed),<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;\" > for uniform linear motion (constant speed for the 3.0 seconds of reaction time), and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=v%2At%2Ba%2At%5E2%2F2 ALIGN=MIDDLE  ALT=\"d=v%2At%2Ba%2At%5E2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > for uniformly accelerated linear motion (the braking part). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );