To determine which graph best represents the relationship between velocity and time, we can break down the motion described in the problem:

1. Negative acceleration for 2 seconds:

   • The velocity decreases over time during this period. The slope of the velocity-time graph is negative, meaning the graph should be sloping downward for 2 seconds.

2. Constant velocity for 1 second:

   • The velocity remains unchanged, so the graph should be a flat horizontal line for the next 1 second.

3. Positive acceleration for 3 seconds:

   • The velocity increases over time during this period. The slope of the velocity-time graph is positive, meaning the graph should be sloping upward for 3 seconds.

Conclusion:

The velocity-time graph will look like this:

• First segment (0 to 2 seconds): A downward-sloping line (representing negative acceleration).
• Second segment (2 to 3 seconds): A flat, horizontal line (representing constant velocity).
• Third segment (3 to 6 seconds): An upward-sloping line (representing positive acceleration).

So, the correct graph will show these three phases:

1. A line sloping down for the first 2 seconds,
2. A horizontal line for the next 1 second,
3. A line sloping up for the final 3 seconds.

Would you like a more detailed explanation, or do you have any specific questions?

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Here are some related questions to explore:

1. What does the slope of a velocity-time graph represent?
2. How can you calculate displacement from a velocity-time graph?
3. How does a graph of acceleration vs. time look for this motion?
4. How do different types of motion affect velocity-time graphs?
5. How can you tell if an object is decelerating or accelerating from a velocity-time graph?

Tip: The area under a velocity-time graph represents displacement, which is useful for finding how far an object has traveled.