Final answer:
In mathematics, when solving for an unknown variable such as number $w without having time variable t, an equation that does not include t is used. Solution (b) requires using the equation $w² = wo² + 2a0, while solution (a) uses the equation $w = wo + at. Choosing the right equation is key to solving these types of problems.
Step-by-step explanation:
The situation described is one where Winnie has a number $w, and we are tasked with matching different mathematical contexts with the appropriate expressions that represent those situations. When dealing with a situation where certain variables are given, and one needs to be determined, the selection of the proper equation is critical. If a time variable t is not given, as in solution (b), an equation that does not include t must be used. In this case, $w² = wo² + 2a0 is appropriate because it does not contain the variable t, and all other variables are known, allowing us to solve for $w.
On the other hand, solution (a) indicates that when both acceleration a and time t are given and the final velocity $w needs to be calculated, the equation $w = wo + at should be used. Here, $w is already isolated, making it straightforward to find its value.
Understanding which equation to use is comparable to understanding sentence structure in English. Just as words need to be arranged in a specific order to make sense, numbers and variables need to be arranged according to mathematical rules to find a solution.