document.write( "Question 1033818: Please help me with this problem:
\n" ); document.write( "A particle moves along the x axis so that its velocity at time t, t > 0, is given by v(t) = $\"%28t+-+2%29%2Ft\"$ . If the particle's position at t = 1 is x = 10, write an equation which describes the position of the particle as a function of t.
\n" ); document.write( " Also, what velocity does the particle approach as t get large? \n" ); document.write( "

Algebra.Com's Answer #648489 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
To find the position, integrate the velocity.
\n" ); document.write( " $\"v%28t%29=1-2%2Ft\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"x%28t%29=int%28%28v%28t%29%29%2Cdt%29\"$
\n" ); document.write( " $\"x%28t%29=int%28%281-2%2Ft%29%2Cdt%29\"$
\n" ); document.write( " $\"x%28t%29=t-ln%28t%29%2BC\"$
\n" ); document.write( "So when $\"t=1\"$ ,
\n" ); document.write( " $\"1-ln%281%29%2BC=10\"$
\n" ); document.write( " $\"1%2BC=10\"$
\n" ); document.write( " $\"C=9\"$
\n" ); document.write( " $\"highlight%28x%28t%29=t-ln%28t%29%2B9%29\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "When $\"t-%3Einfinity\"$ ,
\n" ); document.write( " $\"v%28t%29=1-0\"$
\n" ); document.write( " $\"v%28t%29=1\"$
\n" ); document.write( " \n" ); document.write( "

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