An object falls freely near our surface, which graph best represents the relationship between objects, kinetic energy and time elapsed during it’s fall.
The relationship between an object's kinetic energy and time elapsed during its fall can be represented by a quadratic graph.
As the object falls freely near the surface, its kinetic energy will increase due to the conversion of potential energy. However, it will eventually reach a maximum value when it reaches terminal velocity and the force of air resistance equals the force of gravity. At this point, the kinetic energy remains constant, leading to a plateau in the graph.
Therefore, the best graph representing this relationship would be a concave-upward parabolic curve. The vertical axis represents the object's kinetic energy, while the horizontal axis represents the time elapsed during the fall. The curve starts at zero kinetic energy at the beginning of the fall, steadily increases, and eventually levels off at a maximum value.
(Note: It is important to note that this graph assumes no external forces other than gravity and air resistance acting on the object during its fall near the surface.)
The relationship between an object's kinetic energy and time elapsed during its fall can be represented by a linear graph. As the object falls freely near the surface, its potential energy is converted into kinetic energy, and its speed increases as it falls.
The kinetic energy of an object is given by the equation:
KE = (1/2)mv^2
Where:
KE represents the kinetic energy,
m represents the mass of the object, and
v represents the velocity of the object.
Since the velocity of a freely falling object increases linearly with time, we can substitute v with (gt), where g is the acceleration due to gravity and t represents the time elapsed.
Therefore, the equation for kinetic energy becomes:
KE = (1/2)m(gt)^2
Simplifying this equation:
KE = (1/2)m(g^2)(t^2)
The relationship between kinetic energy (KE) and time (t) is quadratic, meaning it increases with the square of time.
So, the best graph representation for this relationship would be a parabolic curve, where the y-axis represents kinetic energy and the x-axis represents the time elapsed.
To determine the relationship between an object's kinetic energy and the time elapsed during its fall, we need to recall the principles of free fall and kinetic energy.
First, in free fall near the surface of the Earth, the object experiences a constant acceleration due to gravity, which we typically denote as "g." It means that the object's speed increases by the same amount every second. The acceleration due to gravity is approximately 9.8 m/s^2.
Now, let's consider the formula for kinetic energy:
Kinetic Energy (KE) = 1/2 * mass * velocity^2
Since the object is falling freely, its initial velocity is zero. As it falls, its velocity increases due to gravity. Therefore, the kinetic energy also increases.
Based on these principles, the relationship between the object's kinetic energy and the time elapsed during its fall can be represented by a quadratic function. This means that the graph will be a parabola.
The x-axis would represent time elapsed, and the y-axis would represent the object's kinetic energy. Initially, when the time is zero, the kinetic energy is also zero. As time passes, the kinetic energy increases quadratically until it reaches its maximum value.
Hence, the graph that best represents the relationship between an object's kinetic energy and time elapsed during its fall is a parabolic curve that starts at zero, increases rapidly at first, and then more gradually as time goes on.