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# 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?

###### FREE Expert Solution

Law of conservation of energy:

$\overline{)\begin{array}{rcl}{\mathbf{K}}_{\mathbf{i}}\mathbf{+}{\mathbf{U}}_{\mathbf{i}}& {\mathbf{=}}& {\mathbf{K}}_{\mathbf{f}}\mathbf{+}{\mathbf{U}}_{\mathbf{f}}\\ \frac{\mathbf{1}}{\mathbf{2}}\mathbf{m}{{\mathbf{v}}_{\mathbf{i}}}^{\mathbf{2}}\mathbf{+}\mathbf{q}{\mathbf{V}}_{\mathbf{i}}& {\mathbf{=}}& \frac{\mathbf{1}}{\mathbf{2}}\mathbf{m}{{\mathbf{v}}_{\mathbf{f}}}^{\mathbf{2}}\mathbf{+}\mathbf{q}{\mathbf{V}}_{\mathbf{f}}\end{array}}$

The final speed of the proton is:

vf = vi/3 = (3.9 × 105)/3 = 1.3 × 105 m/s

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###### 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?

What scientific concept do you need to know in order to solve this problem?

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