Final Speed of a Proton Accelerated by Potential Difference V: Velocity Formula

[koujidaisuki76]

A proton of mass m and charge e is acclerated from rest through a potential difference V. The final speed of the proton is: ?

I tried to figure this out.. but I can't find the equation for this.

thank you

 

[mezarashi]

A common definition for electric potential (voltage) is the work done per unit charge (or Joules per Coulomb) to move a charge from infinity to a point in an electric field.

With that knowledge, how much energy was transferred to this proton of charge e?

Knowing that the proton of mass m was initially at rest, and has now gained some kinetic energy E, what is it's speed?

 

[koujidaisuki76]

so then answer is 2Ve/m...?

 

[koujidaisuki76]

i get 2q/m... how does voltage apply to the answer?

 

[Astronuc]

A charge of q accelerated across a potential V will have a change in energy of delta(E) = qV. If at rest, the change in energy is equal to the change in kinetic energy, assuming it is non-relativistic, which is a reasonable assumption in the case.