There is a uniform spherically symmetric surface charge density at a distance $$R_0$$ from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed $$V(R(t))$$ of the distribution as a function of its instantaneous radius $$R(t)$$ is:

$$U_{\text{initial}} + K_{\text{initial}} = U_{\text{final}} + K_{\text{final}}$$

$$\frac{1}{4\pi\varepsilon_0}\frac{Q^2}{2R_0} + 0 = \frac{1}{4\pi\varepsilon_0}\frac{Q^2}{2R(t)} + \frac{1}{2}M [V(R(t))]^2$$

$$[V(R(t))]^2 = \frac{Q^2}{4\pi\varepsilon_0 M}\left(\frac{1}{R_0} - \frac{1}{R(t)}\right)$$

$$V(R(t)) = \sqrt{\frac{Q^2}{4\pi\varepsilon_0 M}} \cdot \sqrt{\frac{1}{R_0} - \frac{1}{R(t)}}$$

At $$R(t) = R_0$$, the speed $$V = 0$$.

As $$R(t) \to \infty$$, the speed approaches a finite maximum value $$V_0 = \sqrt{\frac{Q^2}{4\pi\varepsilon_0 M R_0}}$$.

The functional dependency on $$R(t)$$ describes a curve that rises steeply at first and gradually flattens out, asymptotically approaching $$V_0$$.