# Problem: A proton has an initial speed of 3.9 × 105 m/s.What potential difference is required to reduce the initial speed of the proton by a factor of 3?_____ kV

###### FREE Expert Solution

Electrical potential energy:

$\overline{){\mathbf{U}}{\mathbf{=}}{\mathbf{q}}{\mathbf{V}}}$

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{E}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}}$

vf = v0/3

U0 = qV0

Uf = qVf

KE0 = (1/2)mv02

KEf = (1/2)mvf2 = (1/2)m(v0/3)2 = (1/18)mv02

###### Problem Details

A proton has an initial speed of 3.9 × 105 m/s.

What potential difference is required to reduce the initial speed of the proton by a factor of 3?
_____ kV