Question
Which graph Best represents the relationship between velocity and time for an object that accelerates uniformly for 2 seconds, then moves constant velocity for 1 seconds, and finally decelerates for 3 seconds?
Answers
GPT-4o mini
To represent the relationship between velocity and time for the scenario you described, we can break it down into three segments:
1. **Uniform Acceleration for 2 Seconds**: During this phase, the velocity increases linearly. If we assume the object starts from rest, the graph will show a straight line with a positive slope.
2. **Constant Velocity for 1 Second**: In this segment, the velocity remains constant, which means the graph will feature a horizontal line.
3. **Deceleration for 3 Seconds**: During deceleration, the object’s velocity decreases linearly over time. This will be represented by a straight line with a negative slope on the graph.
Putting all of these segments together, the graph will look like:
- An upward-sloping line (indicating increasing velocity) for the first 2 seconds.
- A horizontal line at the peak velocity for the next 1 second.
- A downward-sloping line (indicating decreasing velocity) for the last 3 seconds.
The graph would thus have three distinct sections: the first section has a positive slope, the second section is flat (constant), and the third section has a negative slope. The overall shape of the graph resembles a trapezoid or a piecewise linear function when plotted against time.
1. **Uniform Acceleration for 2 Seconds**: During this phase, the velocity increases linearly. If we assume the object starts from rest, the graph will show a straight line with a positive slope.
2. **Constant Velocity for 1 Second**: In this segment, the velocity remains constant, which means the graph will feature a horizontal line.
3. **Deceleration for 3 Seconds**: During deceleration, the object’s velocity decreases linearly over time. This will be represented by a straight line with a negative slope on the graph.
Putting all of these segments together, the graph will look like:
- An upward-sloping line (indicating increasing velocity) for the first 2 seconds.
- A horizontal line at the peak velocity for the next 1 second.
- A downward-sloping line (indicating decreasing velocity) for the last 3 seconds.
The graph would thus have three distinct sections: the first section has a positive slope, the second section is flat (constant), and the third section has a negative slope. The overall shape of the graph resembles a trapezoid or a piecewise linear function when plotted against time.