Final answer:
The second solution is unacceptable because it lacks dimensional consistency and cannot correctly describe a physical scenario. Chemical equations must also have balanced charges to be considered correct. In quadratic equations, the quadratic formula is used to find solutions to the form ax² + bx + c = 0.
Step-by-step explanation:
The question is asking to identify the physical grounds upon which the second solution to a system of equations is considered unacceptable. In the context provided, the terms of the proposed second solution U1,f = -2.5 m/s, U2,f = 0 are not dimensionally consistent, meaning there is a mismatch in their dimensions which makes the equation not viable in physical terms. If an equation is not dimensionally consistent, it cannot possibly describe a real physical scenario, hence it is referred as "nonsense".
Additionally, as with chemical equations, the balance of charges is crucial, which applies not just to the number of atoms or molecules involved, but also to their charges. A chemical equation can only be correct if both the number types of atoms and the charges are balanced on both sides. An imbalance in charge, as in the provided chemical equation with charges 1+ and 3+, is a clear sign that the equation is not valid.
It is also important to treat equations as precise statements that convey specific concepts, especially in subjects like chemistry and physics, where equations serve as the language describing fundamental laws of nature. When working with equations involving multiple unknowns, we must remember that there need to be as many independent equations as there are unknowns to find a unique solution. Otherwise, the given information is insufficient for a definitive answer unless additional relationships or laws are applied.
Finally, when dealing with a quadratic equation, such as x² + 1.2 x 10⁻²x - 6.0 × 10⁻³, the quadratic formula can be used to find the solutions. This formula is applicable to any equation of the form ax² + bx + c = 0, providing a systematic approach to solving quadratic equations.