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)

Question

Responses

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 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 cannot be calculated from the graph.

Answer 1

To interpret the provided information about the graph of acceleration versus force for the five motorboats, we can use Newton's second law, which states that \( F = ma \) (force equals mass times acceleration).

1. The graph has a slope that indicates a linear relationship between force and acceleration, which confirms that they follow \( F = ma \).
2. Since the y-intercept is zero, this means that if no force is applied, there is no acceleration, which is consistent with the theory.
3. The slope of the line in the graph represents the mass of the motorboats (mass = force/acceleration).

Given that the relationship is linear (with the same slope), this implies that the five motorboats may have different forces and accelerations, but they have the same mass because the slope (mass) is consistent across all tests.

Now, evaluate each statement:

• "All five motorboats have the same final velocity, which can be calculated from the graph." - Not necessarily true since the final velocity depends on both mass and acceleration, but we can’t determine the final velocity directly from this graph alone.

• "All five motorboats have the same mass, which cannot be calculated from the graph." - This is partially true, they do have the same mass, but we can indirectly extract mass information from the slope.

• "All five motorboats have the same mass, which can be calculated from the graph." - This is the correct statement since the slope of the line gives the mass.

• "All five motorboats have the same final velocity, which cannot be calculated from the graph." - Similar to the first statement, this is not necessarily true.

Therefore, the correct answer is:

All five motorboats have the same mass, which can be calculated from the graph.