Graphical Analysis and applied problems

🎯 Class Objective:

The student analyzes and compares motion graphs, identifies key patterns and values, and schematizes the information to transmit clear explanations and support problem-solving in group exercises.

📊 Quantitative Questions — Piecewise Position vs Time Graph

1. What is the total distance traveled from t = 0 s to t = 10 s?

2. What is the total displacement of the object?

3. Calculate the velocity between:

   • a) t = 0 s to t = 2 s

   • b) t = 2 s to t = 4 s

   • c) t = 4 s to t = 6 s

   • d) t = 6 s to t = 8 s

   • e) t = 8 s to t = 10 s

4. During which time interval is the object at rest?
   (Justify using velocity = 0)

5. At what time interval does the object have the greatest velocity?

6. Calculate the average velocity for the entire motion.

7. Calculate the average speed for the entire motion.
   (Compare with average velocity)

8. What is the displacement between t = 2 s and t = 8 s?

9. How far does the object travel between t = 4 s and t = 8 s?

📊 Quantitative Questions — Piecewise Velocity vs Time Graph

1. What is the velocity of the object during each time interval?

2. Calculate the displacement in each interval
   (Use: area under the graph)

   • a) 0–2 s

   • b) 2–6 s

   • c) 6–10 s

3. What is the total displacement from t = 0 s to t = 10 s?

4. What is the average velocity for the entire motion?

5. What is the total distance traveled?

6. At what time does the object cover the first 20 meters?

7. How much displacement occurs between t = 2 s and t = 8 s?

8. Which interval contributes the most to total displacement? Justify quantitatively.