The relationship between kinetic energy (KE) and velocity (v) of an object in motion is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
where \(m\) is the mass of the object and \(v\) is its velocity.
From this equation, we can see that kinetic energy is proportional to the square of the velocity. This means that if you were to graph kinetic energy (on the y-axis) against velocity (on the x-axis), the graph would be a parabola opening upwards, reflecting the quadratic relationship.
If you're looking for a specific graph, you would want to choose one that shows a curve starting from the origin (0,0) and rising steeply, indicating that as velocity increases, the kinetic energy increases more rapidly due to the squared term.
If you have specific graph options, please share them, and I can help identify which one correctly illustrates this relationship.