# An atom moves in a region where potential energy varies: calculating the new velocity

#### polmdm

Alright guys, I'm new here and to physics. I'm self-teaching physical chemistry and am starting with basic physics so I'm stuck on this:

Consider an atom of mass m moving along the x
direction with an initial position x1 and initial speed v1. If the
atom moves for a time interval Δt in a region where the potential
energy varies as V(x), what is its speed v2 at position x2?

v2 = v1[dV(x)/dx]Δt/m

(m = mass)

Can someone explain how that equation is derived?

#### HallsofIvy

You say you are self studying physics but what pre-requisites, what background, do you have? In particular have you taken a Calculus class? Do you know what dv/dx means?

Unfortunately, it looks to me like the equation you have is NOT correct. Are you sure it is not v2= v1+ [dV(x)/dx]Δt/m?

• 2 people

#### topsquark

Forum Staff
Alright guys, I'm new here and to physics. I'm self-teaching physical chemistry and am starting with basic physics so I'm stuck on this:

Consider an atom of mass m moving along the x
direction with an initial position x1 and initial speed v1. If the
atom moves for a time interval Δt in a region where the potential
energy varies as V(x), what is its speed v2 at position x2?

v2 = v1[dV(x)/dx]Δt/m

(m = mass)

Can someone explain how that equation is derived?
Do you know of the equation $$\displaystyle F = - \frac{dV}{dx}$$ where V(x) is the potential energy function?

-Dan

#### polmdm

You say you are self studying physics but what pre-requisites, what background, do you have? In particular have you taken a Calculus class? Do you know what dv/dx means?

Unfortunately, it looks to me like the equation you have is NOT correct. Are you sure it is not v2= v1+ [dV(x)/dx]Δt/m?
I'm not strong with calculus (working on it at the same time now) but I know what dv/dx means haha.
There could very well be a typo...I don't know why it isn't what you put.
Also where does mass come from?

#### polmdm

Do you know of the equation $$\displaystyle F = - \frac{dV}{dx}$$ where V(x) is the potential energy function?

-Dan
Yeah the section introduces that equation but I have no idea how to get from that to the equation I posted. Any thoughts?

thanks!

#### studiot

Yeah the section introduces that equation but I have no idea how to get from that to the equation I posted. Any thoughts?

thanks!
(I also wondered that)

Also please tell us if you have done any dimensional analysis and if so have you tried it on the equation you posted?

Dimensional analysis can quickly and easily identify if an expression is possibly correct or definitely incorrect and can even help deduce new equations/relationships/formulae.

I can tell you that your equation is dimensionally consistent.

I would guess that your equation derives from equating the gain (could be negative) of kinetic energy of the particle to the change in potential energy of the particle, from time t1 to t2 (hence delta t). Calculating the change in potential energy would involve integrating V(x) along the path ie the x axis.

I think that Physical Chemistry is a fascinating subject, but it does require a higher level of maths than 'wet' Chemistry.

A really good and clear book to have for this (study and reference and reference) is

Erich Steiner

The Chemistry Maths Book

Oxford University Press

Here is a clear and simple introduction to Dimensions and a useful table of them in PDF format.

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