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The position of a moving particle along x-axis is measure to be: x(t)=3t^3-13t^2+16t-2; where t>=0;

the question is when the particle is moving in the negative x-direction?

1) I just wanna make sure does that mean the particle reverse the direction of motion, in which case, the answer is abvious:

v=9t^2-26t+16; then find out that the answers would be 8\9 and 2 where 8\9 would be the answer.

2) If the question is asking the specific time that the particle will move in the negative direction:

I have tried three methods which i can not go through:

1. Using long division, i tried to divide this equation by some components such as (t+1), (t-1),

(3t+1) or (3t-1), but i failed.

2. Using Mean theory, f(a)*f(b)<0, and take the 3rd derivative to find the inflection point then approch the answer via mean theory, it's too complicated.

3.Using Newton's method, or Newton-Raphson method, to approch the answer after finding the inflection point, too intricate.

Since the acceleration defined by a linear equation, it's also a little bit impossible to apply the simply physics equations to calculate the answer!!!

Help needed!!!

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Mr. Sasho:

Sorry,there are several grammatical errors, please ignore them, i will eliminate grammatical errors next time to increase the readability.

Thanks for your time!

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The particle is moving in the negative direction of the x-axis when the distance function x(t) is decreasing and that happens when the first derivative v(t) is less than 0, which in turn happens between 8/9 and 2.

[Are you in section L01, 136.151? If yes, and if you study the material (well) before we cover it in the lectures, then the subject of your question is on the edge (and spilling out) of the current scope of this forum. Otherwise it is expected that the questions in this forum are closely related to what we have (already) covered during the lectures. [I would like to avoid misuses by students who are not in our section, not taking our course (or perhaps even not in this university, country, planet,.., at all (which is, as I see, very unlikely in your case).]

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Mr. Sasho:

I'm sorry to cause this misconception, i have no means to offend you or the forum. I have been hasitated for a while and tried to solve it by myself, but i failed. It's just out of my curiosity, i like math, especially the process to solve the puzzle. As a matter of fact, i'm current in your course 136.151 L01 Morning class from 8:30 to 9:20 (M Th F),and i take the notes carefully. All in all, thank you very much to help me get over this barrier!

Have a nice day!

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Nothing in your post was offensive. Your initial question was somewhat unusual (given the stage of this course at the moment); not more than that.

Feel free to ask questions any time.