December 29th, 2010, 04:55 AM  #1 
Senior Member Joined: Oct 2009 Posts: 895 Thanks: 1  when the body's ...
Hi all 1  3 give the positions s = f(t) of a body moving on a coordinate line with s in meters and t in seconds: 1  s = t^2  3t + 2 , [0,2] 2  s = 6t  t^2 , [0,6] 3 s = t^3 + 3t^2  3t , [0,3] a ) When if ever during the interval does the body change direction?  Now I try to solve this 1 to 3 1 ) = 2t  3 then the body will change the direction at x = 0 and x = 1.5 2 )6 2t then the body change it direction at x = 0 3 ) 3t^2 +6t  3 here I got x = 1 and the teacher said here velocity is always negative which means the direction does not change. please help me 
December 29th, 2010, 05:22 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 461 Math Focus: Calculus/ODEs  Re: when the body's ...
1.) , Find the derivative of s with respect to t and equate to zero: Thus, the body changes direction at t = 1.5 2.) , Thus, the body changes direction at t = 3 3.) , Since we have a root of multiplicity 2, we conclude the body does not change direction at t = 1, or at all on the given interval. 
December 29th, 2010, 05:37 AM  #3 
Senior Member Joined: Oct 2009 Posts: 895 Thanks: 1  Re: when the body's ...
Ok ,, thanks


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