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:

v_{f} = v_{i}/3 = (3.9 × 10^{5})/3 = 1.3 × 10^{5} m/s

A proton has an initial speed of 3.9 × 10^{5} m/s.

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

Frequently Asked Questions

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

Our tutors have indicated that to solve this problem you will need to apply the Electric Potential concept. You can view video lessons to learn Electric Potential. Or if you need more Electric Potential practice, you can also practice Electric Potential practice problems.