Question

identify the segments: motion man graph 1. identify the segment(s) of constant velocity 2. identify the segment(s) of only positive velocity 3. identify the segment(s) of only negative velocity 4. identify the segment(s) of both positive and negative velocity 5. identify the segment(s) of positive acceleration 6. identify the segment(s) of negative acceleration 7. identify the segment(s) of no (zero) acceleration 8. estimate the velocity of the object at segment b 9. estimate the velocity of the object at segment d 10. estimate the velocity of the object at segment f 11. estimate the velocity of the object at segment i 12. estimate the velocity of the object at the start of segment a 13. estimate the velocity of the object at the end of segment a 14. estimate the velocity of the object at the start of segment b 15. estimate the velocity of the object at the end of segment b 16. estimate the velocity of the object at the start of segment e 17. estimate the velocity of the object at the end of segment e 18. estimate the velocity of the object at the start of segment g 19. estimate the velocity of the object at the end of segment g 20. estimate the average velocity of the object over segment a 21. estimate the average velocity of the object over segment g

Explanation:

Step1: Recall velocity - time graph concepts

On a velocity - time graph, constant velocity is a horizontal line, positive velocity is above the time - axis, negative velocity is below the time - axis, positive acceleration is an upward - sloping line, negative acceleration is a downward - sloping line, and zero acceleration is a horizontal line or a point.

Step2: Identify constant velocity segments

Segments with a horizontal line on the velocity - time graph have constant velocity. So the segments of constant velocity are B, D, F, I.

Step3: Identify positive velocity segments

Segments above the time - axis have positive velocity. So the segments of only positive velocity are A, B, G, H.

Step4: Identify negative velocity segments

Segments below the time - axis have negative velocity. So the segments of only negative velocity are D, E.

Step5: Identify segments with both positive and negative velocity

Segments that cross the time - axis have both positive and negative velocity. So the segments are C.

Step6: Identify positive acceleration segments

Upward - sloping segments have positive acceleration. So the segments of positive acceleration are G, H.

Step7: Identify negative acceleration segments

Downward - sloping segments have negative acceleration. So the segments of negative acceleration are C.

Step8: Identify zero acceleration segments

Horizontal segments have zero acceleration. So the segments of zero acceleration are B, D, F, I.

Step9: Estimate velocities

• Segment B: The velocity is approximately 6.0 m/s.
• Segment D: The velocity is approximately - 12.0 m/s.
• Segment F: The velocity is approximately 0.0 m/s.
• Segment I: The velocity is approximately 0.0 m/s.
• Start of segment A: The velocity is approximately 0.0 m/s.
• End of segment A: The velocity is approximately 6.0 m/s.
• Start of segment B: The velocity is approximately 6.0 m/s.
• End of segment B: The velocity is approximately 6.0 m/s.
• Start of segment E: The velocity is approximately - 12.0 m/s.
• End of segment E: The velocity is approximately - 12.0 m/s.
• Start of segment G: The velocity is approximately 0.0 m/s.
• End of segment G: The velocity is approximately 6.0 m/s.
• Average velocity over segment A: Since the initial velocity \(u = 0\) m/s and final velocity \(v=6\) m/s, and assuming uniform acceleration (as it is a straight - line segment), the average velocity \(\bar{v}=\frac{u + v}{2}=\frac{0 + 6}{2}=3\) m/s.
• Average velocity over segment G: Since the initial velocity \(u = 0\) m/s and final velocity \(v = 6\) m/s, the average velocity \(\bar{v}=\frac{u + v}{2}=\frac{0+6}{2}=3\) m/s.

Answer:

1. B, D, F, I
2. A, B, G, H
3. D, E
4. C
5. G, H
6. C
7. B, D, F, I
8. 6.0 m/s
9. - 12.0 m/s
10. 0.0 m/s
11. 0.0 m/s
12. 0.0 m/s
13. 6.0 m/s
14. 6.0 m/s
15. 6.0 m/s
16. - 12.0 m/s
17. - 12.0 m/s
18. 0.0 m/s
19. 6.0 m/s
20. 3 m/s
21. 3 m/s