A proton is accelerated from rest through a potential difference $V _ { 0 }$ and gains a speed $v _ { 0 }$. If it were accelerated instead through a potential difference of $2 V _ { 0 }$, what speed would it gain?

Question

Quizplus · Accepted Answer

The kinetic energy gained by the proton is proportional to the potential difference it is accelerated through. Doubling the potential difference doubles the kinetic energy, not the speed. Since kinetic energy is proportional to the square of the speed ($K = \frac{1}{2}mv^2$), doubling the kinetic energy results in the speed increasing by a factor of $\sqrt{2}$, making the correct answer $v_0\sqrt{2}$.

A Proton Is Accelerated from Rest Through a Potential Difference V0V _ { 0 }V0​

A Proton Is Accelerated from Rest Through a Potential Difference $V _ { 0 }$