Physics - Electrical Potential help

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A proton released from rest accelerates through a potential difference V, and its final speed is proportional to the square root of V, or V^(1/2). The relationship is derived from equating the energy gained from the potential difference (q*V) to the kinetic energy (1/2 mv²). To find the final speed, one can set the kinetic energy equal to the energy gained, leading to the equation 1/2 mv² = qV. The Volt is defined as Joules per Coulomb, emphasizing the energy transfer involved. Understanding this relationship is crucial for solving problems related to electrical potential and kinetic energy.
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A proton is released from rest and accelerates through a potential difference V. The final speed of the proton is proportional to the potential difference in which of the following ways?

A. V
B. V^1/2
C. V^-1/2
D. V^-1

I think it is V^(1/2) (just√V) but I am no sure exactly how to find this. Any help would be great. I was thinking that I had to take kinetic energy + potential energy = 0 then kinetic energy= -potential energy. But if this is right what would I do? (1/2)mv²=what? No idea and any help is great. Thanks!
 
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The Volt unit is shorthand for Joules per Coulomb. So a charge q traversing a potential difference V gains (or loses) q*V joules of energy. Equate with kinetic energy and you're there.
 

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