The relationship between kinetic energy (KE) and velocity (v) of an object in motion is given by the kinetic energy formula:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the object and \( v \) is its velocity. According to this formula, kinetic energy is proportional to the square of the velocity. Therefore, if you were to graph kinetic energy (y-axis) against velocity (x-axis), the result would be a quadratic curve starting from the origin (0,0) and increasing as the velocity increases.
So, the correct graph would show a parabolic curve that rises steeply as velocity increases, reflecting the \( v^2 \) dependence of kinetic energy. If you're looking for options, you should look for a graph that shows this parabolic relationship.
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