The kinetic energy of an object that is dropped from rest and falls a distance d is proportional to the distance d itself.

Here's why:

1. The object starts with zero kinetic energy because it is at rest.

2. As the object falls, it gains speed due to the force of gravity. This increases its kinetic energy.

3. The kinetic energy (KE) of an object is given by the equation KE = 1/2 mv^2, where m is the mass of the object and v is its velocity.

4. The velocity of the object is determined by the distance it has fallen and the acceleration due to gravity. The equation for this is v = sqrt(2gd), where g is the acceleration due to gravity and d is the distance fallen.

5. Substituting the equation for v into the equation for KE gives KE = 1/2 m(2gd) = mgd.

6. Therefore, the kinetic energy of the object is directly proportional to the distance d that it has fallen.

Question

The kinetic energy of an object that is dropped from rest and falls a distance d is proportional to the distance d itself.

Here's why:

1. The object starts with zero kinetic energy because it is at rest.

2. As the object falls, it gains speed due to the force of gravity. This increases its kinetic energy.

3. The kinetic energy (KE) of an object is given by the equation KE = 1/2 mv^2, where m is the mass of the object and v is its velocity.

4. The velocity of the object is determined by the distance it has fallen and the acceleration due to gravity. The equation for this is v = sqrt(2gd), where g is the acceleration due to gravity and d is the distance fallen.

5. Substituting the equation for v into the equation for KE gives KE = 1/2 m(2gd) = mgd.

6. Therefore, the kinetic energy of the object is directly proportional to the distance d that it has fallen.

Knowee AI · Accepted Answer

The kinetic energy of an object that is dropped from rest and falls a distance d is proportional to the distance d itself.

Here's why:

1. The object starts with zero kinetic energy because it is at rest.

2. As the object falls, it gains speed due to the force of gravity. This increases its kinetic energy.

3. The kinetic energy (KE) of an object is given by the equation KE = 1/2 mv^2, where m is the mass of the object and v is its velocity.

4. The velocity of the object is determined by the distance it has fallen and the acceleration due to gravity. The equation for this is v = sqrt(2gd), where g is the acceleration due to gravity and d is the distance fallen.

5. Substituting the equation for v into the equation for KE gives KE = 1/2 m(2gd) = mgd.

6. Therefore, the kinetic energy of the object is directly proportional to the distance d that it has fallen.

An object is dropped from rest from a certain height. Air resistance is negligible. After falling a distance d, the object’s kinetic energy is proportional to which of the following?

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