Given, Rest mass of the particle, $m_0 = 10^{-30} \text{ kg}$ Relativistic mass of the particle, $m = 1.25 \times 10^{-30} \text{ kg}$ Speed of light, $c = 3 \times 10^8 \text{ m/s}$ According to the theory of relativity, the relativistic mass is given by: $$ \begin{aligned} m &= \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}} \end{aligned} $$ Rearranging the formula to solve for $v$: $$ \begin{aligned} \sqrt{1 - \frac{v^2}{c^2}} &= \frac{m_0}{m} \\ 1 - \frac{v^2}{c^2} &= \left( \frac{m_0}{m} \right)^2 \\ \frac{v^2}{c^2} &= 1 - \left( \frac{m_0}{m} \right)^2 \end{aligned} $$ Substituting the values: $$ \begin{aligned} \frac{v^2}{c^2} &= 1 - \left( \frac{10^{-30}}{1.25 \times 10^{-30}} \right)^2 \\ &= 1 - \left( \frac{1}{1.25} \right)^2 \\ &= 1 - (0.8)^2 \\ &= 1 - 0.64 \\ &= 0.36 \end{aligned} $$ Now, calculating $v$: $$ \begin{aligned} v &= c \sqrt{0.36} \\ &= 0.6 \times 3 \times 10^8 \text{ m/s} \\ &= 1.8 \times 10^8 \text{ m/s} \end{aligned} $$ Thus, the velocity of the particle is $1.8 \times 10^8 \text{ m/s}$.