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A car is moving along Highway 20 according to the given equation, where $x$ meters is the directed distance of the car from a given point $P$ at $t$ hours. Find the values of $t$ for which the car is moving to the right and when it is moving to the left. Draw a diagram to describe the motion of the car.

motion of car: $x = 2t^3 + 15t^2 + 36t + 2$

So when $x$ is positive it moving right and when $x$ is negative its moving left?

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up vote 1 down vote accepted

I would assume that $x > 0$ corresponds to the right and $x < 0$ corresponds to the left, (if whoever stated the question used a different convention then they can simply swap the answers around, in mathematical physics so long as you state how your signs, or more generally your frame of reference, work then you will be safe).

Using Wolfram Alpha on your polynomial it has a single real root at approximately $x = -0.056894$ and increases monotonically. Therefore the car moves left for $ \infty < t < -0.056894$ and right otherwise (at the root it is niether turning left nor right and makes a transition between the two).

I imagine that the diagram you should draw is $S$ shaped, with $x = -0.056894$ being in the centre of the $S$.

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Just want to make sure, don't know physics very well. – yiyi Nov 7 '12 at 13:09

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