Newton's Laws Unit Test

Question

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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)
Responses

All five motorboats have the same final velocity, which can be calculated from the graph.
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 mass, which can 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 mass, which cannot be calculated from the graph.

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

Answer 1

In the scenario presented, the key piece of information is that the graph is a sloped line with a y-intercept of zero when plotting acceleration versus force. According to Newton's second law of motion, \( F = ma \) (force equals mass times acceleration), a straight line through the origin indicates that there is a linear relationship between force and acceleration.

Since the y-intercept is zero, it implies that all motorboats are experiencing the effects of the same mass across the variations in force applied, as acceleration (a) is proportional to force (F).

Given that all five motorboats have the same mass, the correct response would be:

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

This statement reflects the linear relationship seen in the graph \( (a \propto F) \), allowing one to deduce the mass from the slope of the line, which is equal to 1/mass when force and acceleration are plotted.