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 Post subject: When is the particle moving away from the origin?Posted: Tue, 19 Apr 2011 09:43:22 UTC
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Joined: Wed, 1 Sep 2010 14:17:35 UTC
Posts: 57
Suppose that is the differentiable function of x shown in the accompanying graph.

The position,s at time (sec) of a particle moving along the coordinate line is

meters. When is the particle moving toward the origin? away from the origin?

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 Post subject: Posted: Tue, 19 Apr 2011 11:16:28 UTC
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Joined: Mon, 23 Feb 2009 23:20:33 UTC
Posts: 1049
If s(t) is defined in that way, then f(t) must be the velocity of the particle. It is moving away while f(t) is positive. And it looks like f(t) = -f(2-t), so the trajectory is symmetrical and it returns to the origin without overshooting.

In fact you can (but probably aren't intended to) guess the solution; it looks like , which you can integrate, and then choose a constant to ensure s(0)=0.

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