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October 30th, 2010, 01:46 PM   #1
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velocity of a body moving along the s-axis v = t^2-4t +3 >>

hello !

porticle motion at time t>=0 , the velocity of a body moving along the s-axis
v = t^2-4t +3
a ) Find the body acceleration each time the volicty is zero .
b ) When the body moving forward ? backward ?
c) when is the body's velocity increasing ? deceasing ?

----------- the answer>>>>>

[color=#0000FF]a ) v = 0
2t-4 = 00
t = 2

acceleration = dv/dt = 2

b)
I'm not sure for this answer :
v = (2)^2 -4(2) + 3
= -1

then the body moving backward

c ) body's velocity is deceasing [/color]
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October 30th, 2010, 03:50 PM   #2
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Re: velocity of a body moving along the s-axis v = t^2-4t +3

We are given

a) Find the body's acceleration each time the velocity is zero.





Thus, the velocity is zero at t = 1 and t = 3.




b) When is the body moving forward? backward?

v(0) = (-)(-) = positive, moving forward on [0,1)
v(2) = (+)(-) = negative, moving backward on (1,3)
v(4) = (+)(+) = positive, moving forward on (3,?)

c) When is the body's velocity increasing? decreasing?

We equate a(t) to zero, the check the interval(s).

a(t) = 2(t - 2) = 0

a(t) is zero at t = 2.

a(0) = negative, velocity decreasing on [0,2)
a(3) = positive, velocity increasing on (2,?)
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October 30th, 2010, 07:15 PM   #3
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Re: velocity of a body moving along the s-axis v = t^2-4t +3

Hi all

the velocity is zero at t = 1 and t = 3.

why you talke 3

why didny take 1 to 2

?
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October 30th, 2010, 07:34 PM   #4
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Re: velocity of a body moving along the s-axis v = t^2-4t +3

Well, part (a) asks what the acceleration is when the velocity is zero. Factoring the given v(t) we find



Thus, the velocity is zero when t = 1 and t = 3. So we use those values for t in a(t) which we find by differentiating v(t) with respect to t, which is

2 is not a zero for v(t), but it is a zero for a(t), which tells us when the velocity changes the sign of its rate of change.

Graph of velocity:

Graph of acceleration:
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October 30th, 2010, 11:19 PM   #5
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Re: velocity of a body moving along the s-axis v = t^2-4t +3

I forget how we can get (t-1 ) (t-3 ) = 0 helo ne in this step .
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October 31st, 2010, 01:30 AM   #6
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Re: velocity of a body moving along the s-axis v = t^2-4t +3

thanks now I understand all
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