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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 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.
All five motorboats have the same final velocity, which cannot 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 mass, which cannot be calculated from the graph.
All five motorboats have the same mass, which cannot be calculated from the graph.

1 answer

To determine the correct statement, let's analyze the information provided.

The graph shows a linear relationship between acceleration and force, and the y-intercept is zero. This suggests that the relationship is consistent with Newton's second law of motion, which states that \( F = ma \) (Force = mass × acceleration).

  1. The fact that the line is sloped and passes through the origin indicates that the ratio of force to acceleration (F/a) is constant, which directly implies that the mass (m) for each motorboat must be the same if the slope (which corresponds to mass) is the same for all boats.

  2. The graph does not directly provide information about the final velocity of the boats, as velocity depends on both acceleration and the time over which the acceleration occurs. Without knowing the time or further information regarding the acceleration for a specific duration, we cannot determine the final velocities.

Based on this reasoning, the correct statement is:

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