The graph shown represents a function of height (in feet) versus time (in seconds). From the shape of the graph and the context, this is likely describing the motion of an object that has been launched upward, such as a ball being thrown, under the influence of gravity.

Here's a breakdown of what the intervals represent:

(1) Rising Interval:

• Interval Description: The section labeled (1) shows the object increasing in height over time.
• Interpretation: This represents the upward motion of the object as it rises after being launched. During this interval, the object is slowing down as gravity opposes its upward velocity.
• Key Point: The object's velocity decreases as it approaches its peak.

Peak:

• Point Description: The peak of the graph (the vertex) is the highest point the object reaches.
• Interpretation: At this point, the object's upward velocity becomes zero momentarily before it begins to fall back down.

(2) Falling Interval:

• Interval Description: The section labeled (2) shows the object decreasing in height over time.
• Interpretation: This represents the downward motion of the object as it falls back toward the ground. Gravity accelerates the object downward during this interval.
• Key Point: The velocity of the object increases in the downward direction as it falls.

Would you like a detailed mathematical explanation or equations describing this motion (e.g., kinematic equations)?

5 Related Questions:

1. What is the mathematical function that describes this type of motion?
2. How do we calculate the maximum height of the object based on initial velocity and acceleration?
3. What is the total time the object spends in the air?
4. How would the graph change if air resistance were considered?
5. How do we find the time it takes for the object to reach its maximum height?

Tip:

The motion of this object can be described by quadratic equations derived from the kinematic equations of motion under constant acceleration due to gravity.