Question

different amounts of force are applied to the same boat over several trials, and the acceleration is measured. in a graph of acceleration versus net force, what does the slope of the graph represent? (1 point)
○ the inverse of the speed of the boat
○ the inverse of the mass of the boat
○ the mass of the boat
○ the speed of the boat

Explanation:

To solve this, we use Newton's second law, \( F = ma \), which can be rearranged to \( a=\frac{1}{m}F \). In a graph of \( a \) (acceleration) vs. \( F \) (net force), the equation is in the form \( y = mx + b \) (here, \( y = a \), \( x = F \), and the y - intercept \( b = 0 \)). The slope \( m \) of the line \( a=\frac{1}{m}F \) (where \( m \) here is the mass of the boat) is \( \frac{1}{m} \), which is the inverse of the mass of the boat. We analyze each option:

• "the inverse of the speed of the boat": Speed is not related to the relationship between force and acceleration in this context, so this is incorrect.
• "the inverse of the mass of the boat": As shown by the rearrangement of Newton's second law, the slope of \( a \) vs. \( F \) is \( \frac{1}{m} \) (where \( m \) is the boat's mass), so this is correct.
• "the mass of the boat": The slope is \( \frac{1}{m} \), not \( m \), so this is incorrect.
• "the speed of the boat": Speed has no direct relation to the force - acceleration graph's slope here, so this is incorrect.

Answer:

the inverse of the mass of the boat