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B Acceleration as a function of x to a function of time

  1. Dec 8, 2016 #1
    IMG_1481241036.236074.jpg
     
  2. jcsd
  3. Dec 8, 2016 #2

    BvU

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    In 1 dimension ?
     
  4. Dec 8, 2016 #3
    Yes
     
  5. Dec 8, 2016 #4

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    And is $$F = -\displaystyle {GMm\over x^2} $$ or is $$F = +\displaystyle{GMm\over x^2} $$ as on the whyteboard ?
     
  6. Dec 8, 2016 #5
    Positive
     
  7. Dec 8, 2016 #6

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    Last edited: Dec 8, 2016
  8. Dec 8, 2016 #7
  9. Dec 8, 2016 #8

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    I didn't do anything except enter the thing in wolframalpha !
     
  10. Dec 8, 2016 #9
    So what does that equation mean?
     
  11. Dec 8, 2016 #10

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  12. Dec 8, 2016 #11
  13. Dec 8, 2016 #12
    $$\frac{dv}{dt}=-\frac{GM}{x^2}$$If you multiply both sides of this equation by v=dx/dt, you get:$$v\frac{dv}{dt}=-\frac{MG}{x^2}\frac{dx}{dt}$$Both sides of this equation are exact differentials with respect to time.
     
  14. Dec 8, 2016 #13
    So is the following correct?

    $$v dv = \frac{-MG}{x^2} dx$$
     
  15. Dec 8, 2016 #14
    Yes.
     
  16. Dec 8, 2016 #15

    So how do you integrate over a time interval? That is to say, how do you find the velocity over the interval [0, t]?
     
  17. Dec 8, 2016 #16
    Do you know how to solve for v as a function of x?
     
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