# Graph of Kinetic Energy v. Displacement of a Falling Object

• brendan3eb
In summary, the graph of kinetic energy versus displacement for a falling object in free-fall with an initial horizontal speed of 30 m/s and a starting height of 80 m would be a straight line with negative slope, while the potential energy graph would also be a straight line. This is because both kinetic and potential energy are directly proportional to displacement, as proven through kinematics equations.
brendan3eb
[solved] Graph of Kinetic Energy v. Displacement of a Falling Object

## Homework Statement

Draw and label a graph with energy for the y-axis and displacement for the x-axis of the kinetic energy and potential energy of an object in free-fall that started with a horizontal speed of 30 m/s from a height of 80 m.

U=mgh
k=1/2mv^2

## The Attempt at a Solution

I drew a straight line with negative slope for potential energy because m and g are constants in U=mgh, so it should be a linear graph, as for kinetic energy, I am sitting on the fence on whether or not to draw a straight line or a curve The v^2 makes me want to draw a curve, however, if the the potential energy is a straight line and K = E - U, then shouldn't k be directly proportional to displacement as well?

Last edited:
brendan3eb said:
The v^2 makes me want to draw a curve, however, if the the potential energy is a straight line and K = E - U, then shouldn't k be directly proportional to displacement as well?
Good thinking!

Why not use a bit of kinematics to double check? What's the relationship between v (or v^2) and displacement for a falling object?

ahh..

v^2=v0^2+2a(x-x0)
but since initial velocity in the y direction is 0
v^2=-2g(x-x0)

and since -2g is a constant, v^2 is directly proportional to displacement, and thus kinetic energy is directly proportional to displacement!

Thanks Doc Al!

## 1. What is a graph of kinetic energy v. displacement of a falling object?

A graph of kinetic energy v. displacement of a falling object is a visual representation of the relationship between the kinetic energy of a falling object and its displacement (or distance traveled) as it falls. It shows how the kinetic energy changes as the object falls and can provide valuable information about the motion of the object.

## 2. How is kinetic energy related to displacement of a falling object?

Kinetic energy is directly related to the displacement of a falling object. As the object falls, its displacement increases, and so does its kinetic energy. This is because the object is gaining speed and therefore, its kinetic energy is increasing.

## 3. What is the shape of the graph of kinetic energy v. displacement of a falling object?

The shape of the graph of kinetic energy v. displacement of a falling object is a curved line. It starts at zero kinetic energy when the object is at rest and increases as the object falls, reaching a maximum point when the object is at its maximum displacement. After that, the kinetic energy decreases as the object comes to a stop at the ground.

## 4. How does the mass of a falling object affect the graph of kinetic energy v. displacement?

The mass of a falling object does not affect the shape of the graph of kinetic energy v. displacement. However, a heavier object will have a higher maximum kinetic energy compared to a lighter object, as it has more mass to convert into kinetic energy as it falls.

## 5. What factors can cause variations in the graph of kinetic energy v. displacement of a falling object?

There are a few factors that can cause variations in the graph of kinetic energy v. displacement of a falling object. These include air resistance, the initial speed of the object, and the gravitational pull of the Earth. Air resistance can decrease the kinetic energy by slowing down the object as it falls, while a higher initial speed or stronger gravitational pull can increase the kinetic energy of the falling object.

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