1. **State the problem:** We are given the equation for velocity as a function of displacement: $$V_f^2 = V_i^2 + 2ax$$ where: - $V_f$ is the final velocity, - $V_i$ is the initial velocity, - $a$ is the acceleration, - $x$ is the displacement. 2. **Formula explanation:** This formula comes from the equations of motion in physics, specifically when acceleration is constant and time is not directly involved. 3. **Important rules:** - The velocities are squared. - Displacement $x$ can be positive or negative depending on direction. - Acceleration $a$ is constant. 4. **Example calculation:** Suppose $V_i = 5$, $a = 3$, and $x = 4$. Find $V_f$. 5. **Substitute values:** $$V_f^2 = 5^2 + 2 \times 3 \times 4$$ $$V_f^2 = 25 + 24$$ $$V_f^2 = 49$$ 6. **Solve for $V_f$:** $$V_f = \sqrt{49}$$ $$V_f = 7$$ 7. **Interpretation:** The final velocity is 7 units (same units as initial velocity). This formula allows you to find the final velocity after moving a displacement $x$ under constant acceleration $a$, starting from initial velocity $V_i$.