A proton is accelerated from rest through a potential difference V₀ and gains a speed v₀.If it were accelerated instead through a potential difference of 2V₀,what speed would it gain?

Question

Quizplus · Accepted Answer

The kinetic energy gained by the proton is directly proportional to the potential difference, according to the equation E = qV. Thus, if the potential difference is doubled, the kinetic energy gained will also double. Since the kinetic energy gained is given by (1/2)mv^2, and the mass of the proton does not change, the speed gained will increase proportionally to the square root of the kinetic energy gained. Therefore, the speed gained in the new potential difference will be v1√2 = v₀√2.

A Proton Is Accelerated from Rest Through a Potential Difference 2\sqrt { 2 }2​

A Proton Is Accelerated from Rest Through a Potential Difference $\sqrt { 2 }$