To determine which graph best represents the relationship between an object's kinetic energy and the time elapsed during its free fall, we need to consider how kinetic energy changes as the object falls.
When an object falls freely under the influence of gravity, its velocity increases due to the acceleration imparted by gravity (approximately \(9.81 , m/s^2\) near Earth's surface). 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 (constant during the fall),
- \(v\) is the velocity of the object, which increases over time as the object accelerates.
Since the velocity increases linearly with time (because of the constant acceleration due to gravity), the kinetic energy, which depends on the square of the velocity, will increase quadratically with time.
Therefore, the graph that correctly represents the relationship between kinetic energy and time should show an exponential increase (or a parabolic shape) for kinetic energy as time increases.
You would need to provide the graphs (A, B, C, D) for a specific comparison. However, look for a graph where the kinetic energy increases in a non-linear and accelerating manner as time progresses, indicating a quadratic relationship.