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 a graph that relates the forces of the motors to their accelerations, we can refer to Newton's second law of motion, which states that \( F = ma \), where \( F \) is the force, \( m \) is the mass of the motorboat, and \( a \) is the acceleration.
If the forces are plotted on the y-axis and the accelerations on the x-axis, the equation can be rearranged to the form of a linear equation:
\[ F = m \cdot a \]
This shows that the relationship is linear and the y-intercept is the value of \( F \) when \( a = 0 \). Since if there is no acceleration (meaning the motorboat is stationary or moving at constant velocity), the force acting on the boat would also be zero (assuming no external forces like friction or drag), the y-intercept of this graph would be:
**zero**
So, the correct response is **zero**.
If the forces are plotted on the y-axis and the accelerations on the x-axis, the equation can be rearranged to the form of a linear equation:
\[ F = m \cdot a \]
This shows that the relationship is linear and the y-intercept is the value of \( F \) when \( a = 0 \). Since if there is no acceleration (meaning the motorboat is stationary or moving at constant velocity), the force acting on the boat would also be zero (assuming no external forces like friction or drag), the y-intercept of this graph would be:
**zero**
So, the correct response is **zero**.