select the graph that shows the correct relationship between kinetic energy and speed. hint: if one object…

select the graph that shows the correct relationship between kinetic energy and speed. hint: if one object is moving at 2 times the speed of a second object and the objects have the same mass, then the first object has 4 times the kinetic energy of the second object.

select the graph that shows the correct relationship between kinetic energy and speed. hint: if one object is moving at 2 times the speed of a second object and the objects have the same mass, then the first object has 4 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 mass $m$ is constant, $K$ is proportional to $v^{2}$. This is a quadratic relationship.

Step2: Analyze the shape of the graph

A quadratic function $y = ax^{2}$ ($a>0$ in this case since $\frac{1}{2}m>0$) has a parabolic shape. As the speed $v$ increases, the kinetic energy $K$ increases non - linearly.

Answer:

The graph with a parabolic shape (the third graph from the left and bottom - left in the set of four graphs) shows the correct relationship between kinetic energy and speed.