The relationship between kinetic energy (KE) and velocity (v) of an object in motion is given by the equation:
\[ KE = \frac{1}{2} mv^2 \]
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 if you were to plot kinetic energy on the y-axis and velocity on the x-axis, the graph would show a parabolic curve opening upwards.
To summarize, the correct graph would be a curve that starts at the origin (0,0) and rises steeply as the velocity increases, reflecting the quadratic relationship between kinetic energy and velocity.
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