Final answer:
The task involves finding the curve length, identifying a tangent's slope (velocity), calculating distance and displacement, and determining a pendulum's period, which involves derivatives, integration, and application of formulas over time.
Step-by-step explanation:
The student's question involves finding the curve length over a certain interval, identifying a tangent to a curve at a specific time point, and then using this information along with velocity and acceleration data to calculate distance and displacement of a truck over a 15 second interval. Additionally, there's mention of calculating the period of a pendulum, which is a separate problem, but it ties into the topic of using functions to describe physical quantities over time. Below are the steps commonly used to solve such problems:
- Identify the relevant equations that describe the curve, velocity, or acceleration.
- Use given data points to find specific values such as the slope of the tangent line (velocity).
- Integrate or apply the appropriate formulas to find the desired quantities such as curve length, distance, or displacement.
- For physical systems like a pendulum, apply the specific formula that relates period to other variables like length and gravitational acceleration, ensuring that the conditions for using the formula (e.g., small angle deflection) are met.
This approach would generally involve taking derivatives to find slopes at specific points (tangents) and possibly integrating to find the total distance or displacement.