An incorrect universe

In one imaginary universe two charges $$q_1$$ and $$q_2$$, both of mass 1 g, obey the following inverse cube law instead of Coulomb's law

$\large{ \vec{F} = k_e\frac{q_1q_2 }{|r_{21}|^3} } \hat{r_{21}}$

In this universe, the two charges $$q_1 = 1\mu C$$ and $$q_2=-1\mu C$$ are placed at $$-1$$ m and $$1$$ m on the x-axis, respectively. The charges are released from rest at $$t=0$$. Find the time $$\tau$$ in seconds at which they collide.

Assumptions and Details

• $$K_e = 9\times10^9 \frac{m^2}{F}$$
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