Substitute the given values into the kinetic energy formula: $100 \, \text{J} = \frac{1}{2} \times (2 \, \text{kg}) \times v^2$. This simplifies to $100 = 1 \times v^2$, so $v^2 = 100$. Taking the square root of both sides gives $v = 10 \, \text{m/s}$ (since speed is a magnitude and must be non-negative).