1. **State the problem:** We want to find the acceleration $a$ using the kinematic equation $$v^2 = v_0^2 + 2ad$$ where $v$ is the final velocity, $v_0$ is the initial velocity, $a$ is acceleration, and $d$ is displacement. 2. **Given values:** - Final velocity $v = 0$ - Initial velocity $v_0 = 30$ - Displacement $d = 75$ 3. **Substitute the values into the formula:** $$0^2 = 30^2 + 2a(75)$$ 4. **Simplify the equation:** $$0 = 900 + 150a$$ 5. **Solve for $a$:** Subtract 900 from both sides: $$-900 = 150a$$ Divide both sides by 150: $$a = \frac{-900}{150} = -6$$ 6. **Interpretation:** The acceleration $a$ is $-6$ m/s$^2$, which means the object is decelerating (slowing down) at 6 m/s$^2$. **Final answer:** $$a = -6 \text{ m/s}^2$$