document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=973015>Question 973015</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-15t^2-60ln(t + 1)<BR>\n" );
document.write( "where t > 0 is the time in seconds.<BR>\n" );
document.write( "(a) Find a function that describes the speed of the rocket.<BR>\n" );
document.write( "(b) What is the distance covered by the rocket by time t = 6 seconds?<BR>\n" );
document.write( "(c) Find the value of time t when the speed of the rocket is 100 ms&#1048576;^-1<BR>\n" );
document.write( "(d) Find a function that describes the acceleration of the rocket<BR>\n" );
document.write( "(e) Find the acceleration of the rocket at t = 3 seconds. <BR>\n" );
document.write( "(f) Find the time when the rocket's acceleration is &#1048576;-15ms^-&#1048576;2. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #595292 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=595292\">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-15t^2-60ln(t + 1)<BR>\n" );
document.write( "where t > 0 is the time in seconds.<BR>\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) What is the distance covered by the rocket by time t = 6 seconds?<BR>\n" );
document.write( "s(t) = 220t-15t^2-60ln(t + 1)<BR>\n" );
document.write( "s(6) = 220*6 - 15*36 - 60/7 = 771.43 meters<BR>\n" );
document.write( "---------------------------<BR>\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( "Solve for t, ignore the negative value.<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "(d) Find a function that describes the acceleration of the rocket<BR>\n" );
document.write( "a = 2nd derivative<BR>\n" );
document.write( "s\"(t) = -30 + 60/(t+1)^2<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "(e) Find the acceleration of the rocket at t = 3 seconds.<BR>\n" );
document.write( "s\"(t) = -30 + 60/16 = -26.25 m/sec/sec<BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "(f) Find the time when the rocket's acceleration is &#1048576;-15ms^-&#1048576;2.<BR>\n" );
document.write( "Not clear.   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );