The displacement-time graph of particle is shown in Fig....

The displacement-time graph of particle is shown in Fig. $4.17 .$ (A) Work done by all the forces in part $O A$ is greater than zero (B) Work done by all the forces in part $A B$ is greater than zero (C) Work done by all the forces in part $B C$ is greater than zero (D) Work done by all the forces in part $A B$ is less than zero

The displacement-time graph of particle is shown in Fig. $4.17 .$
(A) Work done by all the forces in part $O A$ is greater than zero
(B) Work done by all the forces in part $A B$ is greater than zero
(C) Work done by all the forces in part $B C$ is greater than zero
(D) Work done by all the forces in part $A B$ is less than zero

Key Concepts

Work Done by a Force

Work is defined as the product of the force acting on an object and the displacement of the object in the direction of the force. It is a measure of energy transfer due to force application. Whether work is positive or negative is determined by the angle between the force and displacement vectors: work is positive when the force has a component in the direction of displacement and negative when it opposes it.

Displacement?Time Graph Analysis

A displacement–time graph is a graphical representation of an object's displacement as a function of time. The slope of the graph at any point provides information about the object's velocity, and changes in the slope indicate acceleration or deceleration. This tool helps in visualizing the motion of the object, including periods of constant motion, speeding up, or slowing down, which are essential for analyzing the work done during different phases of the motion.

Work–Energy Theorem

The work–energy theorem states that the net work done on an object is equal to its change in kinetic energy. This principle links force, displacement, and the energetic state of a system. By analyzing the changes in kinetic energy over segments of motion (as illustrated in parts of the displacement–time graph), one can infer the net work done by the forces acting on the object.

Kinetic Energy Changes in Motion Segments

Changes in kinetic energy during different intervals of motion reflect the net work done on the object. An increase in kinetic energy implies that the net work is positive, while a decrease implies negative net work. By examining various segments of a displacement–time graph and the corresponding changes in the slope (i.e., velocity), one can identify intervals where energy is being added to or removed from the system.

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