12. Which graph BEST represents the relationship between velocity and time for an object that accelerates uniformly for 2 seconds, then moves at a constant velocity for 1 second, and finally decelerates for 3 seconds?
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I apologize, but as an AI text-based model, I am unable to create or display images or graphs. However, I can describe the relationship between velocity and time for the given scenario.
Initially, the object accelerates uniformly for 2 seconds. In this case, the graph of velocity versus time would show a steady increase in velocity with time.
After 2 seconds, the object moves at a constant velocity for 1 second. In this case, the graph of velocity versus time would be a straight horizontal line, indicating a constant velocity.
Finally, the object decelerates for 3 seconds. The graph of velocity versus time would show a steady decrease in velocity over the 3-second duration.
Overall, the graph would consist of a section with increasing velocity, followed by a section with a constant velocity, and finally a section with decreasing velocity.
The best graph that represents the relationship between velocity and time for this scenario would be as follows:
The graph would consist of three segments:
1. An increasing line segment from time 0 to 2 seconds, representing the acceleration phase.
2. A horizontal line segment from time 2 to 3 seconds, representing the constant velocity phase.
3. A decreasing line segment from time 3 to 6 seconds, representing the deceleration phase.
The graph would resemble a V shape, with the acceleration and deceleration phases forming the two arms of the V, and the constant velocity phase forming the bottom of the V.
To determine the best graph that represents the relationship between velocity and time for the given scenario, we need to understand the different phases of motion that the object goes through:
1. Acceleration: The object accelerates uniformly for 2 seconds.
2. Constant Velocity: The object moves at a constant velocity for 1 second.
3. Deceleration: The object decelerates for 3 seconds.
Taking this information into account, we can analyze the characteristics of each phase:
1. Acceleration: During this phase, the velocity of the object increases at a constant rate. The graph representing this phase would have a positive slope, indicating an increase in velocity over time.
2. Constant Velocity: This phase implies that the object maintains a constant velocity. The graph representing this phase would have a horizontal line, indicating no change in velocity over time.
3. Deceleration: The object decelerates during this phase, meaning its velocity decreases at a constant rate. The graph representing this phase would have a negative slope, indicating a decrease in velocity over time.
Considering these characteristics, the best graph that represents the given scenario would be a graph with a positive slope for the first 2 seconds, followed by a horizontal line for 1 second, and finally a negative slope for 3 seconds.
The graph would start with a positive slope to represent the acceleration phase, then remain horizontal to represent the constant velocity phase, and then end with a negative slope to represent the deceleration phase.
There are several types of graphs that could represent this scenario, such as line graphs or curve graphs. It would depend on the specific mathematical equation that describes the motion accurately.