Question: A particle is set in motion at time \(t=0\) and moves to the right along the \(x\) -axis. (a) Suppose that its acceleration at time \(t\) is \(a=100 e^{-t} .\) Show that the particle moves infinitely far to the right along the \(x\) -axis. (b) Suppose that its acceleration at time \(t\) is \(a=100(1-t) e^{-t} .\) Show that the particle never moves beyond a certain point to the right of its initial position and find that point. Explain why the particle "effectively" comes to a stop at that point.

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