To determine the correct graph for the relationship between an object's kinetic energy and the time elapsed during its free fall, we can use the following physics concepts:
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Kinetic Energy (KE): The kinetic energy of an object is given by the formula: \[ KE = \frac{1}{2} mv^2 \] where \(m\) is the mass of the object and \(v\) is its velocity.
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Velocity of a Free-Falling Object: For an object in free fall (neglecting air resistance), the velocity \(v\) increases linearly with time \(t\) according to the equation: \[ v = gt \] where \(g\) is the acceleration due to gravity (approximately \(9.81 , m/s^2\) near the Earth's surface).
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Kinetic Energy in Terms of Time: By substituting \(v = gt\) into the kinetic energy formula, we get: \[ KE = \frac{1}{2} m (gt)^2 = \frac{1}{2} mg^2 t^2 \] This shows that kinetic energy is proportional to the square of time (\(t^2\)).
Given these relationships, we can conclude that the graph representing the relationship between kinetic energy and time would show a parabolic increase (quadratic relationship) rather than a linear increase or any other shape.
Therefore, the correct graph is one that exhibits a parabolic curve starting at the origin, showing that as time increases, kinetic energy increases with the square of time. Without the actual images of the graphs you're referencing, I can't specify which letter corresponds to the correct one, but make sure you're looking for a graph that shows this parabolic relationship.