Final answer:
The query involves mathematical computations such as solving quadratic equations and applying the quadratic formula. The information provided is fragmented, indicating that the student is likely working on problems related to projectile motion or evaluating functions.
Step-by-step explanation:
The information provided suggests a student is dealing with a variety of mathematical equations and procedures, including evaluating a function, solving a quadratic equation, and understanding concepts related to kinematics and integration by parts. The quadratic equation seems to be a recurring theme, typically of the form at² + bt + c = 0 with different values for a, b, and c. Solutions to these equations can be found using the quadratic formula, which is necessary for solving problems related to projectile motion or finding the time it takes for an object to reach a certain height when thrown upwards.
Unfortunately, the information provided is fragmented and lacks clear context, which makes it difficult to provide a specific answer. It is essential to have a clear and complete question or equation to provide an accurate and helpful response.