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- Thread starter Phys_Boi
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BvU

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In 1 dimension ?

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BvU

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BvU

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Pity: https://www.wolframalpha.com/input/?i=x''+=+1/x^2

(The minus sign gave an analytical solution https://www.wolframalpha.com/input/?i=x''+=+-1/x^2 showing that it isn't an easy differential equation )

(The minus sign gave an analytical solution https://www.wolframalpha.com/input/?i=x''+=+-1/x^2 showing that it isn't an easy differential equation )

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Pity: https://www.wolframalpha.com/input/?i=x''+=+1/x^2

(The minus sign gave an analytical solution https://www.wolframalpha.com/input/?i=x''+=+-1/x^2 showing that it isn't an easy differential equation )

Thanks for this.. how did you get this though? I'm only half way through calc one..

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BvU

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I didn't do anything except enter the thing in wolframalpha !

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BvU

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Perhaps you did mean a minus sign ?

https://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation#Modern_form

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Perhaps you did mean a minus sign ?

https://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation#Modern_form

But doesn't the sign just determine direction?

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Chestermiller

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So is the following correct?

$$v dv = \frac{-MG}{x^2} dx$$

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Chestermiller

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Yes.So is the following correct?

$$v dv = \frac{-MG}{x^2} dx$$

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Yes.

So how do you integrate over a time interval? That is to say, how do you find the velocity over the interval [0, t]?

- #16

Chestermiller

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Do you know how to solve for v as a function of x?So how do you integrate over a time interval? That is to say, how do you find the velocity over the interval [0, t]?

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