Use the graph of velocity vs. time for an object to answer the question.

Question

A line graph that displays the change in velocity over time and is broken up into 3 segments. At zero seconds, the velocity is zero meters per second. At 60 seconds, the velocity is 8 meters per second. The time difference between zero and 60 seconds represents the first segment. At 150 seconds, the velocity is 14 meters per second. The time difference between 60 and 150 seconds represents the second segment. At 240 seconds, the velocity is 29 meters per second. The time difference between 150 and 240 represents the third segment. 
Which statement fairly compares segment 2 and segment 3?

(1 point)
Responses

Segments 2 and 3 have different periods of time, but the force acting in each segment is the same during each period of time. 
Segments 2 and 3 have different periods of time, but the force acting in each segment is the same during each period of time.

Segments 2 and 3 have different periods of time and the force during segment 2 is different than the force during segment 3. 
Segments 2 and 3 have different periods of time and the force during segment 2 is different than the force during segment 3.

Segments 2 and 3 have equal periods of time but the force during segment 2 is different than the force during segment 3. 
Segments 2 and 3 have equal periods of time but the force during segment 2 is different than the force during segment 3.

Segments 2 and 3 have equal periods of time and the force acting in each segment is the same during each period of time.

GPT-4o mini · Answer

To analyze the segments based on the velocity vs. time graph you've described, let's evaluate the details for segments 2 and 3.

Segment 2: This segment runs from 60 seconds (velocity = 8 m/s) to 150 seconds (velocity = 14 m/s). The time duration is \(150 - 60 = 90\) seconds. The change in velocity during this segment is \(14 - 8 = 6\) m/s.
Segment 3: This segment runs from 150 seconds (velocity = 14 m/s) to 240 seconds (velocity = 29 m/s). The time duration is \(240 - 150 = 90\) seconds. The change in velocity during this segment is \(29 - 14 = 15\) m/s.

Now, let's apply the concept of force to these segments. According to Newton's second law (\(F = ma\)), the force acting on an object is related to the mass of the object and its acceleration. Acceleration can be calculated as the change in velocity divided by the time taken.

Acceleration in Segment 2:

Change in velocity = \(6\) m/s
Time = \(90\) seconds
Acceleration = \(\frac{6 \text{ m/s}}{90 \text{ s}} = 0.067 \text{ m/s}^2\)

Acceleration in Segment 3:

Change in velocity = \(15\) m/s
Time = \(90\) seconds
Acceleration = \(\frac{15 \text{ m/s}}{90 \text{ s}} = 0.167 \text{ m/s}^2\)

Given that the acceleration is different in segments 2 and 3, we'll conclude that the force must also be different, assuming the object's mass remains constant.

Now, let's evaluate the provided statements:

Segments 2 and 3 have different periods of time, but the force acting in each segment is the same during each period of time.
Segments 2 and 3 have different periods of time, but the force acting in each segment is the same during each period of time.
Segments 2 and 3 have different periods of time and the force during segment 2 is different than the force during segment 3.
Segments 2 and 3 have equal periods of time but the force during segment 2 is different than the force during segment 3.
Segments 2 and 3 have equal periods of time and the force acting in each segment is the same during each period of time.

Based on our analysis, Segments 2 and 3 have equal periods of time but the force during segment 2 is different than the force during segment 3 (since the accelerations differ, which indicates different forces).

Thus, the best statement that compares segment 2 and segment 3 is:

"Segments 2 and 3 have equal periods of time but the force during segment 2 is different than the force during segment 3."