1. The problem is to understand and use the equation of motion: $$v^2 = u^2 + 2as$$ where $v$ is the final velocity, $u$ is the initial velocity, $a$ is the acceleration, and $s$ is the displacement. 2. This formula is used when acceleration is constant and relates the velocities, acceleration, and displacement without involving time. 3. To use this formula, you need to know three of the four variables to find the unknown one. 4. For example, if you want to find the final velocity $v$, rearrange the formula: $$v = \sqrt{u^2 + 2as}$$ 5. If you want to find displacement $s$, rearrange as: $$s = \frac{v^2 - u^2}{2a}$$ 6. When simplifying fractions, cancel common factors carefully, for example: $$s = \frac{\cancel{v^2} - \cancel{u^2}}{2a}$$ (if applicable). 7. Always check the units and signs of acceleration and displacement to ensure correct results. This formula is fundamental in kinematics for solving motion problems with constant acceleration.