Question

Five motorboats are being tested to see which reaches the highest velocity in the sameamount of time. After graphing the acceleration versus force for each motorboat, the graph is asloped line with a
y
-intercept of zero. Which statement is correct about these motorboats?
(1 point)
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.
All five motorboats have the same final velocity, which can be calculated from the graph.

Answer 1

To analyze the given scenario, we can start by applying Newton's second law of motion, which states that \( F = ma \) (force equals mass times acceleration).

Given that the graph is a straight line with a y-intercept of zero, this suggests that:

- The relationship between acceleration (a) and force (F) is linear, meaning that as force increases, acceleration also increases proportionally.
- The slope of the line represents the mass of the motorboats since \( a = \frac{F}{m} \).

If the y-intercept is zero, it indicates that when no force is applied, there is no acceleration, which is consistent with Newton's laws.

Now let's analyze each of the statements provided:

1. **"All five motorboats have the same mass, which can be calculated from the graph."** - This statement is true. Since the line is straight and has a consistent slope, it indicates that all motorboats have the same mass. The slope (which is \( \frac{1}{m} \)) can be calculated from the graph.

2. **"All five motorboats have the same final velocity, which cannot be calculated from the graph."** - This statement is misleading because the final velocity depends on the time of acceleration and the specific acceleration of each motorboat, which isn’t provided by the graph.

3. **"All five motorboats have the same mass, which cannot be calculated from the graph."** - This statement is incorrect. The mass can be calculated from the slope of the acceleration vs. force graph.

4. **"All five motorboats have the same final velocity, which can be calculated from the graph."** - This statement is incorrect. The final velocity cannot be calculated solely from the graph since it requires information about the time duration over which they accelerate.

Based on this analysis, the correct statement is:

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