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

1. Dec 8, 2016

2. Dec 8, 2016

BvU

In 1 dimension ?

3. Dec 8, 2016

Yes

4. Dec 8, 2016

BvU

And is $$F = -\displaystyle {GMm\over x^2}$$ or is $$F = +\displaystyle{GMm\over x^2}$$ as on the whyteboard ?

5. Dec 8, 2016

Positive

6. Dec 8, 2016

BvU

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

8. Dec 8, 2016

BvU

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

9. Dec 8, 2016

Phys_Boi

So what does that equation mean?

10. Dec 8, 2016

BvU

11. Dec 8, 2016

Phys_Boi

12. Dec 8, 2016

Staff: Mentor

$$\frac{dv}{dt}=-\frac{GM}{x^2}$$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.

13. Dec 8, 2016

Phys_Boi

So is the following correct?

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

14. Dec 8, 2016

Staff: Mentor

Yes.

15. Dec 8, 2016

Phys_Boi

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. Dec 8, 2016

Staff: Mentor

Do you know how to solve for v as a function of x?