Particle moving in potential.

1. Aug 14, 2014

LagrangeEuler

If I have particle moving in the potential $V(x)$, when I write equation of motion
$\frac{dx}{dt}=-V'(x)+q(t)$
and when I integrate this equation do I need to look $V'(x)$ as function of time, or I just could write
$x(t)=-V'(x)t+\int^t_0q(t)dt$

2. Aug 14, 2014

Einj

It depends on how V is defined. According to what you wrote V=V(x) is just a function of space and hence you are correct.

Anyway, what's q(t)? And how did you obtain that equation of motion?

3. Aug 14, 2014

LagrangeEuler

Yes but $x=x(t)$ and $V=V(x)$. So I am confused. But because $V(x)$ is potential I think that I write equation in correct form. This is potential in which particle moves.

4. Aug 14, 2014

ShayanJ

It seems you're using kind of a "constant of differentiation"(like a constant of integration) which is mathematically wrong!!!
You should add a constant only when you integrate something, not when you differentiate something!!!

5. Aug 14, 2014

Orodruin

Staff Emeritus
No, you are not allowed to integrate the equations of motion like that. Even if V does not depend explicitly on time, it does so implicitly through x.

6. Aug 15, 2014

LagrangeEuler

Yes but you know. Particle is moving in some potential $V(x)$. In certain moment $t$ it has coordinate $x(t)$. $q(t)$ is certain pulse. How do you write down this solution?

7. Aug 15, 2014

ShayanJ

Well...You can't write the solution without knowing what is q(t)!

8. Aug 15, 2014

ShayanJ

Well...You can't write the solution without knowing what is q(t)!

Also the following is wrong.
Because x is an unknown function of time so you can't integrate. That's called a differential equation and it has its own methods.