1. The problem is to understand and use the equation of motion: $v^2 = u^2 + 2as$. 2. This formula relates the final velocity $v$, initial velocity $u$, acceleration $a$, and displacement $s$ of an object moving with constant acceleration. 3. The formula is derived from the equations of motion and is useful when time is not known. 4. To use this formula, you need to know three of the four variables to find the unknown one. 5. For example, if you want to find the final velocity $v$, rearrange the formula: $$v = \sqrt{u^2 + 2as}$$ 6. Remember, the square root can have positive and negative values, but in physics, velocity direction matters, so choose the sign based on context. 7. If you want to find displacement $s$, rearrange as: $$s = \frac{v^2 - u^2}{2a}$$ 8. When simplifying fractions, show canceled terms, for example: $$s = \frac{\cancel{v^2} - \cancel{u^2}}{2a}$$ (if applicable). 9. This formula assumes constant acceleration and straight-line motion. 10. Always check units to ensure consistency (e.g., meters, seconds).