select the graph that shows the correct relationship between kinetic energy and mass.\nhint: if one object…

select the graph that shows the correct relationship between kinetic energy and mass.\nhint: if one object has 2 times the mass of a second object and their speeds are the same, then the first object has 2 times the kinetic energy of the second object.

select the graph that shows the correct relationship between kinetic energy and mass.\nhint: if one object has 2 times the mass of a second object and their speeds are the same, then the first object has 2 times the kinetic energy of the second object.

Answer

Explanation:

Step1: Recall kinetic - energy formula

The kinetic - energy formula is $K = \frac{1}{2}mv^{2}$. When the speed $v$ is constant, $K$ is directly proportional to $m$ (since $\frac{1}{2}v^{2}$ is a constant). A direct - proportional relationship between two variables $y$ and $x$ has the form $y = kx$ (where $k$ is a non - zero constant), and its graph is a straight line passing through the origin.

Step2: Analyze the graphs

The first two graphs are non - linear (curved), which do not represent a direct - proportional relationship. The third graph is a straight line passing through the origin, which is consistent with the direct - proportional relationship between kinetic energy $K$ and mass $m$ when speed $v$ is constant.

Answer:

The third graph (the straight - line graph passing through the origin) shows the correct relationship between kinetic energy and mass when the speed is constant.