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

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 different periods of time, but the force acting in each segment is the same during each period of time.

Answer 1

To analyze the segments in the velocity vs. time graph you described:

1. Segment 1 (0 to 60 seconds):

   • Starts at 0 m/s and ends at 8 m/s.
   • Time duration = 60 seconds.
   • Velocity change = 8 m/s.

2. Segment 2 (60 to 150 seconds):

   • Starts at 8 m/s and ends at 14 m/s.
   • Time duration = 150 - 60 = 90 seconds.
   • Velocity change = 14 m/s - 8 m/s = 6 m/s.

3. Segment 3 (150 to 240 seconds):

   • Starts at 14 m/s and ends at 29 m/s.
   • Time duration = 240 - 150 = 90 seconds.
   • Velocity change = 29 m/s - 14 m/s = 15 m/s.

Comparison of Segment 2 and Segment 3:

• Time duration of Segment 2 = 90 seconds.
• Time duration of Segment 3 = 90 seconds (both segments are equal in duration).
• Force is related to acceleration (change in velocity over time). The acceleration in each segment is different:
  • Acceleration in Segment 2: \( \frac{6 , \text{m/s}}{90 , \text{s}} = \frac{1}{15} , \text{m/s}^2 \)
  • Acceleration in Segment 3: \( \frac{15 , \text{m/s}}{90 , \text{s}} = \frac{1}{6} , \text{m/s}^2 \)

Since the periods of time for segments 2 and 3 are equal, but the forces acting (since they are proportional to the acceleration) are different, the correct response is:

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