select the graph that shows the correct relationship between kinetic energy and mass. hint: if one object…
select the graph that shows the correct relationship between kinetic energy and mass. hint: 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 formula for kinetic energy is $K = \frac{1}{2}mv^{2}$, where $K$ is kinetic energy, $m$ is mass and $v$ is speed. When speed $v$ is constant, $K$ is directly proportional to $m$ (since $\frac{1}{2}v^{2}$ is a constant in this case). A direct - proportional relationship is represented by a straight - line graph of the form $y = kx$ (here $y = K$, $x = m$ and $k=\frac{1}{2}v^{2}$).
Step2: Analyze the graphs
The first graph is a non - linear (parabolic) graph, the second graph shows an inverse relationship, the fourth graph is a non - linear decreasing graph. The third graph is a straight - line graph which represents a direct proportionality between kinetic energy and mass when speed is constant.
Answer:
The third graph (the one with a straight - line increasing relationship between kinetic energy and mass)