1. **Problem Statement:** A ball rolls across a smooth surface at a steady speed of 0.5 m/s. We need to find its acceleration. 2. **Understanding the problem:** Acceleration is the rate of change of velocity with respect to time. If the velocity is constant, the acceleration is zero. 3. **Formula:** Acceleration $a$ is given by $$a = \frac{\Delta v}{\Delta t}$$ where $\Delta v$ is the change in velocity and $\Delta t$ is the change in time. 4. **Given:** The ball moves at a steady speed of 0.5 m/s, meaning velocity does not change. 5. **Calculation:** Since velocity is constant, $$\Delta v = 0 \implies a = \frac{0}{\Delta t} = 0$$ 6. **Conclusion:** The acceleration is $0$ m/s$^2$ because the velocity is steady and not changing. **Answer:** a. 0 m/s$^2$