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
the velocity
the velocity
the mass
the mass
zero
zero
Responses
the inverse of the mass
the inverse of the mass
the velocity
the velocity
the mass
the mass
zero
zero
Answers
GPT-4o mini
In a force versus acceleration graph, according to Newton's second law (F = ma), the relationship can be rearranged to express acceleration (a) in terms of force (F):
\[ a = \frac{F}{m} \]
When this equation is graphed with force (F) on the x-axis and acceleration (a) on the y-axis, the equation can be rewritten in the form of a linear equation (y = mx + b), where:
- y (acceleration) is on the vertical axis,
- x (force) is on the horizontal axis,
- m (slope) is the inverse of mass (1/m), and
- b (y-intercept) should be zero (when no force is applied, the acceleration is zero).
Thus, the y-intercept of this graph is:
**zero**
\[ a = \frac{F}{m} \]
When this equation is graphed with force (F) on the x-axis and acceleration (a) on the y-axis, the equation can be rewritten in the form of a linear equation (y = mx + b), where:
- y (acceleration) is on the vertical axis,
- x (force) is on the horizontal axis,
- m (slope) is the inverse of mass (1/m), and
- b (y-intercept) should be zero (when no force is applied, the acceleration is zero).
Thus, the y-intercept of this graph is:
**zero**