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PostPosted: Tue, 19 Apr 2011 09:43:22 UTC 
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Suppose that f(x) is the differentiable function of x shown in the accompanying graph.

Image

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

s=\int^t_0 f(x)\ dx

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


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PostPosted: Tue, 19 Apr 2011 11:16:28 UTC 
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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 f(t)=\sin\pi t, which you can integrate, and then choose a constant to ensure s(0)=0.


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