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?
The graph that best represents this relationship is a graph with three distinct sections: an upward sloping line for 2 seconds to represent the acceleration, a flat line at a constant velocity for 1 second, and a downward sloping line for 3 seconds to represent deceleration.
The graph that best represents the relationship between velocity and time for the given scenario can be described as follows:
1. For the first 2 seconds: The object accelerates uniformly. Therefore, the graph will show a straight line with a positive and increasing slope, indicating a positive acceleration.
2. For the next 1 second: The object moves at a constant velocity. This means that the graph will be a horizontal line at the same level as the end point of the previous acceleration.
3. For the last 3 seconds: The object decelerates. This means that the graph will show a straight line with a negative and decreasing slope, indicating a negative acceleration.
To summarize, the graph will have a positive increasing slope for 2 seconds, followed by a horizontal line for 1 second, and then a negative decreasing slope for 3 seconds.
To determine the best graph that represents the relationship between velocity and time for the given scenario, let's break down the different phases of motion:
1. Accelerates uniformly for 2 seconds:
In this phase, the velocity of the object increases at a constant rate. Therefore, the graph should show a straight line with a positive slope, indicating an increasing velocity.
2. Moves at a constant velocity for 1 second:
During this phase, the object maintains a constant velocity, so the graph should display a horizontal line at the previous velocity reached during acceleration.
3. Decelerates for 3 seconds:
In this final phase, the object's velocity decreases at a constant rate. The graph should show a straight line with a negative slope, indicating a decreasing velocity.
Based on this breakdown, the best graph representation would be as follows:
- For the first 2 seconds, a line with a positive slope indicating acceleration.
- Followed by a horizontal line for 1 second at the constant velocity.
- And finally, a line with a negative slope for the last 3 seconds indicating deceleration.
This description corresponds to a graph that looks like an "A" shape, starting at the origin and ending at a lower point.