To determine which graph best represents the relationship between an object's kinetic energy and time elapsed during its free fall near Earth's surface, we need to consider how kinetic energy changes as the object falls.
The kinetic energy (\( KE \)) 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.
In free fall, the velocity of the object increases linearly over time due to the constant acceleration caused by gravity (\( g \approx 9.81 , \text{m/s}^2 \)). Therefore, the velocity as a function of time (\( t \)) can be expressed as:
\[ v = gt \]
Substituting this expression for \( v \) into the kinetic energy formula, we get:
\[ KE = \frac{1}{2} m (gt)^2 = \frac{1}{2} m g^2 t^2 \]
This shows that kinetic energy is proportional to the square of the time elapsed. Thus, the relationship between kinetic energy and time will be a parabolic curve that opens upwards.
So, the graph that best represents the relationship between the object's kinetic energy and time elapsed during its fall will be a curve that increases quadratically (the precise form will depend on the details of the specific graphs you're comparing).
Assuming the typical options, the correct choice would be one that depicts a parabolic increase in kinetic energy as time increases. If you provide the specific graphs labeled A, B, C, and D, I could help you identify the correct one.
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