Gauss Practice (Hard)

Consider two balls of equal radii and masses but opposite charges, distributed uniformly over their volumes. Initially, the balls are at rest and far away from one another. Due to the Coulomb attraction, the balls start moving towards each other. The balls can be treated as charged clouds, that is to say, they can interpenetrate without friction. During the interaction, the maximum speed achieved by the balls is \(v_{max}=10~\text{m}/\text{s}\). What is the magnitude of their maximum acceleration in meters per second squared? The radius of the balls is \(R=1~\text{m}\).

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