A constant force acts on a moving object. The object makes a fixed magnitude of displacement in some direction. In general, in what direction is the displacement that will result in the object traveling with the least kinetic energy after the displacement occurs?

A.The same direction as the force.
B.The direction does not matter.
C.In a direction perpedicular to the plane of the force and the velocity of the object.
D.The opposite direction as the force.
E.Any direction perpendicular to the force.

I am a bit mixed up and thinkingt b/t C or D.. or E!?!? =/

The opposite direction as the force.

The correct answer is D. The displacement that will result in the object traveling with the least kinetic energy after the displacement occurs is in the opposite direction as the force.

When a constant force acts on an object, the work done by the force is given by the equation W = Fd, where W is the work done, F is the force, and d is the displacement. The work done by the force is directly related to the change in kinetic energy of the object.

If the displacement is in the same direction as the force (option A), the work done will be positive, resulting in an increase in kinetic energy. If the displacement is in a direction perpendicular to the plane of the force and the velocity of the object (option C), the work done will be zero, as the force does not do any work. If the displacement is in any direction perpendicular to the force (option E), the work done will also be zero.

Thus, the only option that results in a decrease in kinetic energy is if the displacement is in the opposite direction as the force (option D).

To determine the direction of displacement that will result in the object traveling with the least kinetic energy, let's consider the relationship between the work done by a force and the change in kinetic energy.

According to the work-energy theorem, the work done by a force is equal to the change in kinetic energy of an object. Mathematically, this is expressed as:

Work = Change in Kinetic Energy

For a constant force, the work done is given by:

Work = Force x Displacement x cos(theta)

Where theta is the angle between the direction of the force and the displacement.

Now, considering the possible options:

A. The same direction as the force: If the displacement is in the same direction as the force (theta = 0), then the work done is positive, resulting in an increase in kinetic energy. Therefore, this option does not correspond to the least kinetic energy.

B. The direction does not matter: This is not always true. The direction of displacement does matter, as it affects the angle (theta) and hence the work done.

C. In a direction perpendicular to the plane of the force and the velocity of the object: If the displacement is perpendicular to the force (theta = 90 degrees), the work done is zero. Since no work is done, the kinetic energy of the object remains unchanged. Therefore, this option does correspond to the least kinetic energy.

D. The opposite direction as the force: If the displacement is in the opposite direction to the force (theta = 180 degrees), then the work done is negative, resulting in a decrease in kinetic energy. Therefore, this option does not correspond to the least kinetic energy.

E. Any direction perpendicular to the force: Similar to option C, if the displacement is perpendicular to the force, the work done is zero, resulting in the least kinetic energy.

Based on this analysis, the correct answer is C. In a direction perpendicular to the plane of the force and the velocity of the object.