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 inverse of the mass
the inverse of the mass
zero
zero
the mass
the mass
the velocity
Responses
the inverse of the mass
the inverse of the mass
zero
zero
the mass
the mass
the velocity
Answers
GPT-4o mini
In a graph of the force of the motors (y-axis) versus their accelerations (x-axis), according to Newton's second law of motion, the relationship is given by the equation:
\[ F = ma \]
where:
- \( F \) is the force,
- \( m \) is the mass of the motorboat,
- \( a \) is the acceleration.
If we rearrange this equation to match the form \( y = mx + b \), we have:
\[ F = ma + 0 \]
Here, \( F \) (force) is the dependent variable (y-axis), \( a \) (acceleration) is the independent variable (x-axis), \( m \) (mass) is the slope of the line, and the term \( 0 \) indicates that there is no constant term subtracted from the force.
Thus, the y-intercept of the graph, which corresponds to the value of \( F \) when \( a = 0 \), is **zero**.
So the correct response is:
**zero**
\[ F = ma \]
where:
- \( F \) is the force,
- \( m \) is the mass of the motorboat,
- \( a \) is the acceleration.
If we rearrange this equation to match the form \( y = mx + b \), we have:
\[ F = ma + 0 \]
Here, \( F \) (force) is the dependent variable (y-axis), \( a \) (acceleration) is the independent variable (x-axis), \( m \) (mass) is the slope of the line, and the term \( 0 \) indicates that there is no constant term subtracted from the force.
Thus, the y-intercept of the graph, which corresponds to the value of \( F \) when \( a = 0 \), is **zero**.
So the correct response is:
**zero**