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Find jerk of time varying force

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This gravitational field we move inside has some distance L after which it becomes 0.Before L it is just like any gravitational field. Suppose we move inside that gravitational field.The acceleration we experience depends on the distance from the planet. $$a\sim\frac{1}{r^2}$$

At t=to we enter the gravitational field and assuming the velocity and acceleration was 0 then:

$$x = x_{0}-\frac{1}{6}j(t-t_{0})^3$$

where j is the jerk or

$$\dot{a}\left(t\right)$$

How can we find the jerk?

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3 comment threads

Can't "enter" infinite gravitational field. (4 comments)
I guess I'm a little confused about one of your criteria ("without . . . acceleration"): in this exam... (5 comments)
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Comments on Find jerk of time varying force

I guess I'm a little confused about one of your criteria ("without . . . acceleration"): in this exam...
HDE 226868‭ wrote about 1 year ago:

I guess I'm a little confused about one of your criteria ("without . . . acceleration"): in this example, the object should always experience a non-zero acceleration because the $\sim1/r^2$ relation is only 0 at $r\to\infty$.

Skipping 1 deleted comment.

MissMulan‭ wrote about 1 year ago:

HDE 226868 you are correct i will edit

MissMulan‭ wrote about 1 year ago:

And i have something else in my mind lets just say the initial acceleration is 0.

celtschk‭ wrote about 1 year ago:

If the initial acceleration is zero, then the initial force is zero, and therefore the particle has infinite distance from the central mass (or in other words, there does not exist any place in space where the acceleration is zero — unless we take other gravitating bodies into account). More generally, for any time-independent field, if both the velocity and the acceleration at the beginning are zero, it follows that the particle stays there forever (unless disturbed by an external force).

MissMulan‭ wrote about 1 year ago:

It is an exercise the gravitational field exists only for some r below a limit and a test particle enters somehow(pops into existence) at the edge of the field.

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