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October 30th, 2010, 11:45 AM   #1
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problem in motion Along coordinate line > help me

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October 30th, 2010, 12:05 PM   #2
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Re: problem in motion Along coordinate line > help me

You are given the displacement , where thus






To find where the velocity changes, we first find all points where v = 0 within the given interval.




Thus t = 1 and t = 2 are critical points. So we check point in the three intervals the two critical points divide the given interval into.

v(.5) is positive
v(1.5) is negative
v(2.5) is positive

Thus, the particle changes direction at t = 1 and t = 2.
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October 30th, 2010, 12:38 PM   #3
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Re: problem in motion Along coordinate line > help me

thanks very much now i understand >>>
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October 30th, 2010, 12:42 PM   #4
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Re: problem in motion Along coordinate line > help me

We put those numbers into the velocity function .

Even easier is to put them into its factored form:



and look at the signs of each factor.

for .5 we have

(+)(-)(-) = positive

for 1.5 we have

(+)(+)(-) = negative

for 2.5 we have

(+)(+)(+) = positive

And actually, we don't really need to check since all of the roots are of multiplicity 1, but I thought checking would be helpful to show the change in direction.
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October 30th, 2010, 12:46 PM   #5
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Re: problem in motion Along coordinate line > help me

thanks very much now i understand >>>
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