A proton is accelerated from rest through a potential...

A proton is accelerated from rest through a potential difference of $25700 \mathrm{V}.$
a. What is the kinetic energy of this proton in joules after this acceleration?
b. What is the speed of the proton after this acceleration?

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Key Concepts

Electric Potential Difference

Electric potential difference represents the work done per unit charge in moving a charge between two points in an electric field. It is a measure of the energy available to be converted into other forms, such as kinetic energy, when a charged particle moves through an electric potential difference.

Energy Conversion in Charged Particle Acceleration

When a charged particle, such as a proton, is accelerated by an electric field, the energy provided by the potential difference is transformed into kinetic energy. This conversion is quantified by the relationship KE = qV, where KE is the kinetic energy, q is the charge of the particle, and V is the potential difference, illustrating how an electrical input translates directly into mechanical motion.

Kinetic Energy and Speed Relationship

The kinetic energy gained by a moving particle can be used to determine its speed using the equation KE = ½mv², where m is the mass of the particle and v is its speed. This relationship is fundamental in mechanics as it connects the energy acquired by the particle with its velocity, allowing for the prediction of its motion under energy conservation principles.

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