Question

five motorboats are being tested to see which reaches the highest velocity in the same amount of time. after graphing the acceleration versus force for each motorboat, the graph is a sloped line with a y-intercept of zero. which statement is correct about these motorboats? (1 point)

all five motorboats have the same final velocity, which can be calculated from the graph.

all five motorboats have the same mass, which can be calculated from the graph.

all five motorboats have the same final velocity, which cannot be calculated from the graph.

all five motorboats have the same mass, which cannot be calculated from the graph.

Explanation:

1. Recall Newton's second law: \( F = ma \), which can be rearranged as \( a=\frac{1}{m}F \). This is in the form of a linear equation \( y = mx + b \), where \( y=a \), \( x = F \), the slope \( m=\frac{1}{M} \) (mass \( M \) of the motorboat), and the y - intercept \( b = 0 \).
2. For a linear graph of \( a \) vs. \( F \) with a y - intercept of zero, the slope is constant. Since the slope \( \text{slope}=\frac{1}{M} \), a constant slope implies that \( \frac{1}{M} \) is constant, so the mass \( M \) of each motorboat is the same.
3. The slope of the \( a - F \) graph is \( \frac{1}{M} \), so we can calculate the mass \( M=\frac{1}{\text{slope}} \) from the graph.
4. Final velocity depends on acceleration and time (\( v = u+at \), assuming initial velocity \( u = 0 \), \( v=at \)). Even though the mass (and thus the relationship between \( a \) and \( F \)) is the same, the force applied (and thus the acceleration) could be different for each motorboat during the test, so we can't conclude about the final velocity from the \( a - F \) graph alone.

Answer:

B. All five motorboats have the same mass, which can be calculated from the graph.