Question
Several motorboats with the same mass are used in an experiment. The forces of the different motors versus their accelerations are graphed. What is the y-intercept of this graph? (1 point)
Responses
the mass
the mass
the velocity
the velocity
the inverse of the mass
the inverse of the mass
zero
Responses
the mass
the mass
the velocity
the velocity
the inverse of the mass
the inverse of the mass
zero
Answers
GPT-4o mini
In the context of the graph of forces exerted by different motors versus their accelerations, we can use Newton's second law, which states that \( F = ma \), where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration.
If we rearrange this equation to express force in terms of acceleration, we can write:
\[ F = m \cdot a \]
This implies that if we were to graph force (F) on the y-axis and acceleration (a) on the x-axis for a constant mass (m), the equation can be interpreted as:
\[ F = m \cdot a \Rightarrow F = m \cdot a + 0 \]
In this equation, the slope of the graph would be the mass (m), and the y-intercept would be zero because when acceleration \( a = 0 \), the force \( F \) is also \( 0 \).
Thus, the y-intercept of the graph is **zero**.
If we rearrange this equation to express force in terms of acceleration, we can write:
\[ F = m \cdot a \]
This implies that if we were to graph force (F) on the y-axis and acceleration (a) on the x-axis for a constant mass (m), the equation can be interpreted as:
\[ F = m \cdot a \Rightarrow F = m \cdot a + 0 \]
In this equation, the slope of the graph would be the mass (m), and the y-intercept would be zero because when acceleration \( a = 0 \), the force \( F \) is also \( 0 \).
Thus, the y-intercept of the graph is **zero**.