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. From this equation, we can see that kinetic energy is proportional to the square of the velocity. This means that as the velocity increases, the kinetic energy increases with the square of that velocity.
Therefore, if you were looking at a graph of kinetic energy (y-axis) versus velocity (x-axis), the correct graph would be a parabolic curve that starts at the origin (0,0) and rises steeply as the velocity increases. It would not be a straight line because the relationship is quadratic, not linear.
If you have options to choose from, look for a graph that shows this upward curving relationship.
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