document.write( "Question 1142313: Calculus Question\r
\n" ); document.write( "\n" ); document.write( "5. A particle moves according to the law of motion $\"+s=t%5E3-12t%2B3%2C+t%E2%89%A50+\"$ , where t is measured in seconds and s in feet. Find the total distance traveled by the particle in the
\n" ); document.write( "first 3 seconds.\r
\n" ); document.write( "\n" ); document.write( "(a) 21ft.
\n" ); document.write( "(b) 22ft.
\n" ); document.write( "(c) 23ft.
\n" ); document.write( "(d) 24ft.
\n" ); document.write( "(e) None of these are correct \n" ); document.write( "

Algebra.Com's Answer #763071 by ikleyn(52780) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "The figure below shows the plot of the given function.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "And now your (and my) task is to read and to interpret this plot correctly.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From the plot and from the function, you can see that the particle starts from the position s= 3 at t= 0 and first moves\r\n" );
document.write( "in direction of NEGATIVE s.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Plot y = \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It reaches minimum negative value s= -13 at t= 2; then it changes the direction of moving and moves in direction of POSITIVE s.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     How did I determine it ? - By taking derivative of the function over \"t\", \r\n" );
document.write( "     equating it to zero and finding the turning point moment at t= 2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Its final position is s= -6 at t= 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the DISPLACEMENT of the particle from t= 0 to t= 3 is only 3 - (-6) = 9 ft;\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "but the total way length, or total traveled way is from s= 3 to s= -13 (16 ft) PLUS from -13 to -6 (7 ft).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In all, the traveled distance is 16 + 7 = 23 ft.    ANSWER  (c)\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );