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December 29th, 2010, 03:55 AM   #1
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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
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December 29th, 2010, 04:22 AM   #2
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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.
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December 29th, 2010, 04:37 AM   #3
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Re: when the body's ...

Ok ,, thanks
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