Calculating Speed of Charged Particles in Electric Field: An Example"

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Two charged particles, one positively and one negatively charged, each with a mass of 5.3 x 10^-3 kg, are initially 0.75 m apart and at rest. Upon release, they accelerate towards each other due to their opposite charges. The potential energy between them converts into kinetic energy as they move closer. To find their speed when the separation is halved, the potential energy difference can be equated to the total kinetic energy of both particles. The discussion emphasizes the importance of energy conservation in calculating their speeds without needing a time variable.
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Two particles each have a mass of 5.3 10-3 kg. One has a charge of +5.0 10-6 C, and the other has a charge of -5.0 10-6 C. They are initially held at rest at a distance of 0.75 m apart. Both are then released and accelerate toward each other. How fast is each particle moving when the separation between them is one-half its initial value?


ok, I know:
q1 = +5.0 x 10^-6 C
q2 = -5.0 x 10^-6 C
r = 0.75m
m = 5.3 x 10^-3 kg

Since they are opposite charges they will atract each other.

I can't seem to figure out where to begin on what formula to use to discover the speed without any time.
 
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the fastest way would be transfering the potential energy difference to kinetic energy.

\Delta U=\frac{mv^2}{2}+\frac{mv^2}{2}

if they didn't have the same mass you had to use the momentum conservation eq. aswell.
 
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