Two identical electric point dipoles have dipole moments ${\overrightarrow{\mathrm{P}}}_1=\mathrm{P}\widehat{\mathrm{i}}$ and  ${\overrightarrow{\mathrm{P}}}_2=-\mathrm{P}\widehat{\mathrm{i}}$ and are held on the $x$ axis at distance $\text{'}a\text{'}$  from each other.  When released, they move along the x-axis with the direction of their dipole moments remaining, unchanged.  If the mass of each dipole is  $\text{'}\mathrm{m}\text{'}$, their speed when they are infinitely far apart is:

Electric field at the location of 2nd dipole due to 1st dipole is  ${\overrightarrow{\mathrm{E}}}_1=\frac{1}{4\mathrm{\pi }{\in }_{\mathrm{o}}}\frac{2\mathrm{P}}{{\mathrm{a}}^3}\widehat{\mathrm{i}}$
So potential energy is    $\mathrm{U}=-{\overrightarrow{\mathrm{P}}}_2.{\overrightarrow{\mathrm{E}}}_1 =\frac{1}{4\mathrm{\pi }{\in }_{\mathrm{o}}}\times \frac{2{\mathrm{P}}^2}{{\mathrm{a}}^3}=\frac{{\mathrm{P}}^2}{2\mathrm{\pi }{\in }_{\mathrm{o}}{\mathrm{a}}^3}$
When they will be infinitely far apart U= 0 and if final speed of each dipole is $v$  , then kinetic energy is  $\frac{1}{2}{\mathrm{mv}}^2+\frac{1}{2}{\mathrm{mv}}^2={\mathrm{mv}}^2$
  $$\begin{gathered} \mathrm{Using} \mathrm{conservation} \mathrm{of} \mathrm{energy}: \\ {\mathrm{K}}_{\mathrm{f}}-{\mathrm{K}}_{\mathrm{i}}={\mathrm{U}}_{\mathrm{i}}-{\mathrm{U}}_{\mathrm{f}} \\ \Rightarrow {\mathrm{mv}}^2=\frac{{\mathrm{P}}^2}{2\mathrm{\pi }{\in }_{\mathrm{o}}{\mathrm{a}}^3} \\ \Rightarrow \mathrm{v}=\frac{\mathrm{P}}{\mathrm{a}}\times \sqrt{\frac{1}{2\mathrm{\pi }{\in }_{\mathrm{o}}\mathrm{ma}}} \end{gathered}$$