1. **State the problem:** We need to find the speed $v$ of an object given its mass $m=4$ kg and kinetic energy $KE=18$ joules. 2. **Formula:** The kinetic energy formula is $$KE = \frac{1}{2} m v^2$$ where $m$ is mass and $v$ is speed. 3. **Substitute known values:** $$18 = \frac{1}{2} \times 4 \times v^2$$ 4. **Simplify the right side:** $$18 = 2 \times v^2$$ 5. **Isolate $v^2$ by dividing both sides by 2:** $$\frac{18}{\cancel{2}} = \cancel{2} \times v^2 \Rightarrow 9 = v^2$$ 6. **Solve for $v$ by taking the square root:** $$v = \sqrt{9} = 3$$ 7. **Answer:** The speed of the object is $3$ meters per second. This corresponds to choice A.