An object falls freely near Earth's surface. Which graph best represents the relationship between the object's kinetic energy and time elapsed during its fall?
A.
B.
C.
D.
C.
The correct graph that represents the relationship between the object's kinetic energy and time elapsed during its fall is graph C. This is because as an object falls freely near Earth's surface, its kinetic energy increases with time. Graph C shows a gradual increase in kinetic energy with time, which is consistent with the concept of an object accelerating due to gravity as it falls.
In order to determine which graph best represents the relationship between the object's kinetic energy and time elapsed during its fall, we need to understand the concept of kinetic energy and how it relates to the object's motion.
Kinetic energy (KE) is the energy possessed by an object due to its motion. It is defined as one-half times the mass (m) of the object multiplied by the square of its velocity (v), expressed mathematically as KE = ½mv^2.
When an object falls freely near Earth's surface, it undergoes accelerated motion due to the force of gravity. As it falls, its velocity increases, leading to an increase in kinetic energy.
From this understanding, we can deduce that as time elapses during the fall, the kinetic energy of the object will also increase, assuming no other external factors are at play.
Examining the given graphs, we can eliminate options A and C immediately as they show a constant or decreasing kinetic energy with respect to time. Since we know that kinetic energy increases as time elapses, these options do not represent the relationship correctly.
Now we are left with options B and D. Both show an increase in kinetic energy with time. However, option B shows a linear increase, while option D shows a curved increase.
Given that the object is freely falling under the influence of gravity, which causes an acceleration towards the Earth, we know that the object's velocity increases non-linearly over time. Since kinetic energy depends on the square of the velocity, we can conclude that option D, which represents a curved increase, best represents the relationship between the object's kinetic energy and time elapsed during its fall.
Therefore, the correct answer is D.