We are to investigate a system of three charges lined up as shown in
the diagram.

The system contains three distinct pairs of charges, two pairs with
charges + and - *q* and separation *d* and one pair with equal
charges *q* and separation 2*d. *Thus the energy is:

Before | After | |

PE | -3kq^{2}/2d_{0} |
-3kq^{2}/d_{0} |

KE | 0 | 2(mv^{2}/2)= mv^{2} |

Total | -3kq^{2}/2d_{0} |
mv^{2}-3kq^{2}/d_{0} |

Setting the totals equal, we find: