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 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 mass, which cannot be calculated from the graph.

Answer 1

To analyze the situation, let's consider the relationship between acceleration, force, and mass based on Newton's second law, which is stated as:

\[ F = m \cdot a \]

where:

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

In the given scenario, the graph of acceleration versus force is a linear relationship with a y-intercept of zero, indicating that as the force increases, the acceleration increases proportionally. This linear relationship suggests that the slope of the line (which is \( \frac{a}{F} \)) represents \( \frac{1}{m} \), meaning the mass of the boats can be derived from this slope.

1. If the slope is the same for all five motorboats, this implies that they all have the same mass.
2. However, since we only have the force and acceleration relationship, we cannot calculate the final velocities directly from this graph without additional information such as the time or distance traveled.

Putting this all together, the correct statement regarding these motorboats is:

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

This option is based on the consistent slope (which can indicate a common mass if the slope is uniform across all trials).