1. Position vs. Time Graph

• Description: The position-time graph shows the elevator’s height (position) as a function of time.
• Explanation:
  • Initially, the elevator starts from rest at the ground floor. The position is zero.
  • During the trip, the elevator accelerates, and the position increases more rapidly, causing a slight curve upward at the beginning.
  • Once the elevator reaches a constant velocity, the position increases linearly with time.
  • As the elevator approaches the 50th floor, it decelerates, making the graph curve downward until it stops at the 50th floor.
  • On the return trip, the elevator descends. Initially, it accelerates, causing the position to decrease faster (downward curve).
  • After reaching a constant speed, the position decreases linearly.
  • Finally, the elevator decelerates when nearing the ground floor, producing a gentle curve as the position returns to zero.

Key Features:

• Two curved sections (acceleration and deceleration).
• Two linear sections (constant velocity).
• Starts and ends at zero.

2. Velocity vs. Time Graph

• Description: This graph shows how the velocity of the elevator changes over time.
• Explanation:
  • The elevator starts at rest (zero velocity).
  • During the initial acceleration, velocity increases linearly, reaching a constant velocity.
  • The velocity remains constant while the elevator is moving upward at a steady speed (flat section).
  • As the elevator decelerates nearing the 50th floor, velocity decreases back to zero.
  • The elevator then starts descending. The velocity becomes negative (downward motion).
  • Initially, velocity decreases (negatively) during acceleration, reaches a negative constant velocity, and finally increases back to zero as the elevator slows to rest at the ground floor.

Key Features:

• Linear rise and fall for acceleration and deceleration.
• Constant positive and negative velocity (flat sections).

3. Acceleration vs. Time Graph

• Description: This graph shows the rate of change of velocity over time.
• Explanation:
  • The elevator experiences positive acceleration at the start when it speeds up (constant positive value).
  • Once at a constant velocity, acceleration is zero.
  • As the elevator approaches the 50th floor, it decelerates, meaning acceleration is negative (constant negative value).
  • After reaching the 50th floor, the elevator starts descending. It accelerates downward, so acceleration is positive again (when moving downward).
  • Constant velocity during the descent shows zero acceleration.
  • Finally, negative acceleration occurs as the elevator decelerates to stop at the ground floor.

Key Features:

• Constant acceleration values during speed changes.
• Zero acceleration during constant velocity.

Summary of Graphs:

1. Position vs. Time: Curves at the start and end (acceleration and deceleration) with linear sections in between (constant speed).
2. Velocity vs. Time: Linear increases and decreases during acceleration and deceleration, with flat sections representing constant velocity.
3. Acceleration vs. Time: Constant positive and negative values during acceleration and deceleration, and zero when the elevator moves at a constant speed.

Would you like a visual representation of these graphs?

---

Relative Questions:

1. How does the slope of the position-time graph relate to velocity?
2. What does the area under the velocity-time graph represent?
3. How would these graphs change if the elevator moved faster?
4. How do acceleration-time and velocity-time graphs relate?
5. What happens to the velocity-time graph if the elevator stops briefly at the 50th floor?

Tip:

In a velocity-time graph, the slope indicates acceleration, while the area under the curve gives the total displacement.