A particle of mass m moves without friction subject to a force F(x) =(adsbygoogle = window.adsbygoogle || []).push({});

−kx + [itex]\frac{kx3}{A2}[/itex], where k and A are positive constants. It is projected

from x = 0 to the positive x direction with initial velocity v0 =

A[itex]\sqrt{\frac{k}{2m}}[/itex]. Find:

(a) the potential energy V (x),

(b) the kinetic energy T(x),

(c) the turning points of the motion.

So I don't know if I am on the right track, I feel I am missing something. For V(x) (potential energy), i got:

[itex]\frac{1}{2}[/itex] kx[itex]^{2}[/itex] - [itex]\frac{1}{4}[/itex] [itex]\frac{kx^{4}}{A^{2}}[/itex]

Then I found T(x) (kinetic energy) to be:

T[itex]_{o}[/itex] - [itex]\frac{1}{2}[/itex]kx[itex]^{2}[/itex] - [itex]\frac{1}{4}[/itex] [itex]\frac{kx^{4}}{A^{2}}[/itex]

I know I am given an initial V[itex]_{o}[/itex], but where would I plug that in to find V(x) or T(x)?

Any help is very much appreciated.

Regards

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Rectilinear motion of a particle

**Physics Forums | Science Articles, Homework Help, Discussion**