document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=971939>Question 971939</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rocket of mass m = 500 kg is travelling in a straight line for a short time.<BR>\n" );
document.write( "The distance in metres covered by the rocket during this time is described<BR>\n" );
document.write( "by the function<BR>\n" );
document.write( "s(t) = 220t - 15t2 - 60 ln (t + 1)\r<BR>\n" );
document.write( "\n" );
document.write( "where t > 0 is the time in seconds.\r<BR>\n" );
document.write( "\n" );
document.write( "a.) Find a function that describes the speed of the rocket.<BR>\n" );
document.write( "b.)Find a function that describes the acceleration of the rocket<BR>\n" );
document.write( "c.)Find the value of time t when the speed of the rocket is 100 ms^&#8722;1\r<BR>\n" );
document.write( "\n" );
document.write( "Amy. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #594373 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=594373\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rocket of mass m = 500 kg is travelling in a straight line for a short time.<BR>\n" );
document.write( "The distance in metres covered by the rocket during this time is described<BR>\n" );
document.write( "by the function<BR>\n" );
document.write( "s(t) = 220t - 15t2 - 60 ln (t + 1)\r<BR>\n" );
document.write( "\n" );
document.write( "where t > 0 is the time in seconds.\r<BR>\n" );
document.write( "\n" );
document.write( "a.) Find a function that describes the speed of the rocket.<BR>\n" );
document.write( "Speed is the 1st derivative.<BR>\n" );
document.write( "s'(t) = 220 - 30t - 60/(t+1)<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "b.)Find a function that describes the acceleration of the rocket<BR>\n" );
document.write( "Accel is the 2nd derivative<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "s\"(t) = -30 + 60/(t+1)^2\r<BR>\n" );
document.write( "\n" );
document.write( "c.)Find the value of time t when the speed of the rocket is 100 m/sec<BR>\n" );
document.write( "s'(t) = 220 - 30t - 60/(t+1) = 100<BR>\n" );
document.write( "30t + 60/(t+1) = 120<BR>\n" );
document.write( "t + 2/(t+1) = 4<BR>\n" );
document.write( "t^2+t 2 = 4t+4<BR>\n" );
document.write( "t^2 - 3t - 2 = 0<BR>\n" );
document.write( "Solve for t, use the positive solution. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );