Question
Five motorboats are being tested to see which reaches the highest velocity in the same amount of time. After graphing the acceleration versus force for each motorboat, the graph is a sloped line with a y-intercept of zero. Which statement is correct about these motorboats?(1 point)
Responses
All five motorboats have the same mass, which cannot be calculated from the graph.
All five motorboats have the same mass, which cannot be calculated from the graph.
All five motorboats have the same mass, which can be calculated from the graph.
All five motorboats have the same mass, which can be calculated from the graph.
All five motorboats have the same final velocity, which can be calculated from the graph.
All five motorboats have the same final velocity, which can be calculated from the graph.
All five motorboats have the same final velocity, which cannot be calculated from the graph.
Responses
All five motorboats have the same mass, which cannot be calculated from the graph.
All five motorboats have the same mass, which cannot be calculated from the graph.
All five motorboats have the same mass, which can be calculated from the graph.
All five motorboats have the same mass, which can be calculated from the graph.
All five motorboats have the same final velocity, which can be calculated from the graph.
All five motorboats have the same final velocity, which can be calculated from the graph.
All five motorboats have the same final velocity, which cannot be calculated from the graph.
Answers
GPT-4o mini
To analyze the graph of acceleration versus force for each motorboat, we can recall Newton's second law of motion, which states that \( F = ma \) (force equals mass times acceleration).
If the graph of acceleration (y-axis) versus force (x-axis) is a straight line with a y-intercept of zero, this indicates a linear relationship between force and acceleration. The slope of this line represents the mass of the motorboats, since the slope can be expressed as:
\[
\text{slope} = \frac{\Delta \text{acceleration}}{\Delta \text{force}} = \frac{a}{F} = \frac{1}{m}
\]
From this information, we can draw the following conclusions:
1. Since the graph is a straight line with zero y-intercept, it indicates that the same mass produces various accelerations in response to different forces applied.
2. All five motorboats would have the same mass if all their graphs coincide perfectly at the origin and have the same slope.
Given the above analysis, it is clear that:
- **All five motorboats have the same mass, which can be calculated from the graph.**
This means the correct response is:
**All five motorboats have the same mass, which can be calculated from the graph.**
If the graph of acceleration (y-axis) versus force (x-axis) is a straight line with a y-intercept of zero, this indicates a linear relationship between force and acceleration. The slope of this line represents the mass of the motorboats, since the slope can be expressed as:
\[
\text{slope} = \frac{\Delta \text{acceleration}}{\Delta \text{force}} = \frac{a}{F} = \frac{1}{m}
\]
From this information, we can draw the following conclusions:
1. Since the graph is a straight line with zero y-intercept, it indicates that the same mass produces various accelerations in response to different forces applied.
2. All five motorboats would have the same mass if all their graphs coincide perfectly at the origin and have the same slope.
Given the above analysis, it is clear that:
- **All five motorboats have the same mass, which can be calculated from the graph.**
This means the correct response is:
**All five motorboats have the same mass, which can be calculated from the graph.**