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 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 can be calculated from the graph.

1 answer

To analyze the scenario, we start with the relationship between force, mass, and acceleration as described by Newton’s second law of motion:

\[ F = m \cdot a \]

Where:

  • \( F \) is the force applied,
  • \( m \) is the mass of the object, and
  • \( a \) is the acceleration.

In the context of the graph provided, with acceleration versus force, we can consider the nature of the line plotted. Since the graph has a y-intercept of zero, it indicates that when no force is applied, the acceleration is also zero. This supports the direct proportionality indicated by \( F = m \cdot a \); if we rearranged it to express acceleration:

\[ a = \frac{F}{m} \]

If this expression gives us a straight line on the graph (acceleration vs. force), then the slope (rise over run) would be \( 1/m \). This means that if the slope is constant for all five motorboats, then they have the same mass.

Given that it is noted that the graphs are straight lines, you can infer that the steepness of these lines (i.e., their slopes) indicates the mass of the motorboats. If each motorboat has a different slope, it would indicate they have different masses. If the slopes are the same, then the masses are equal.

Now, there is no information provided in the prompt about the velocities reached by these boats. The final velocity is determined through time of acceleration and final forces, but this is not quantifiable from the stated graph alone without additional details.

Therefore, the most correct statement based on the information provided is:

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