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 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.) $s(t)=t^2-3t+2$ , $[0,2]$ Find the derivative of s with respect to t and equate to zero: $s'(t)=2t-3=0\:\therefore\:t=\frac{3}{2}$ Thus, the body changes direction at t = 1.5 2.) $s(t)=6t-t^2$ , $[0,6]$ $s'(t)=6-2t=2(3-t)=0\:\therefore\:t=3$ Thus, the body changes direction at t = 3 3.) $s(t)=-t^3+3t^2-3t$ , $[0,3]$ $s'(t)=-3t^2+6t-3=-3(t-1)^2=0$ 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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