Motion in a Force Field A mathematical model for the

Chapter 4, Problem 23E

(choose chapter or problem)

Motion in a Force Field A mathematical model for the position x(t) of a body moving rectilinearly on the x-axis in an inverse-square force field is given b

\(\frac{d^{2} x}{d t^{2}}=-\frac{k^{2}}{x^{2}}\)

Suppose that at \(t=0\) the body starts from rest from the position \(x=x_{0}, \quad x_{0}>0\). Show that the velocity of the body at time t is given by \(v^{2}=2 k^{2}\left(1 / x-1 / x_{0}\right)\). Use the last expression and a CAS to carry out the integration to express time t in terms of x.

Text Transcription:

fracd^2xdt^2=-frack^2x^2

t=0

x=x_0,x_0>0

v^2=2k^21/x-1/x_0

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Becoming a subscriber
Or look for another answer

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back