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 velocity
the velocity
the mass
Responses
the inverse of the mass
the inverse of the mass
zero
zero
the velocity
the velocity
the mass
Answers
GPT-4o mini
In the context of a graph plotting force (y-axis) versus acceleration (x-axis) for several motorboats with the same mass, the relationship is governed by Newton's second law, which states that \( F = ma \).
In the equation \( F = ma \):
- \( F \) is the force (in Newtons),
- \( m \) is the mass (in kilograms),
- \( a \) is the acceleration (in m/s²).
When plotted as Force (y) against Acceleration (x), the equation can be rearranged as:
\[ F = m \cdot a \]
This will yield a straight line graph with:
- a slope equal to the mass \( m \),
- and a y-intercept of 0 when \( a \) is 0 (since if there's no acceleration, there’s no force being applied).
Therefore, the y-intercept of this graph is **zero**.
In the equation \( F = ma \):
- \( F \) is the force (in Newtons),
- \( m \) is the mass (in kilograms),
- \( a \) is the acceleration (in m/s²).
When plotted as Force (y) against Acceleration (x), the equation can be rearranged as:
\[ F = m \cdot a \]
This will yield a straight line graph with:
- a slope equal to the mass \( m \),
- and a y-intercept of 0 when \( a \) is 0 (since if there's no acceleration, there’s no force being applied).
Therefore, the y-intercept of this graph is **zero**.