Question

The area under the force-displacement curve represents
(A) Velocity
(B) Acceleration
(C) Impulse
(D) Work done

Answer 1

Hint: It is known that we can get the area under a curve by integrating it within the given limits. Upon integrating the small area elements under the curve, we will get the final total area of the curve. Here we have the force on one axis of the curve and displacement on the other axis. We have to find what the area under the curve represents.

Complete step by step solution:
Let the force be on the Y-axis and displacement be on the X-axis, as shown below.

The shaded portion represents the area that we are considering.
Here we have a rectangular area. We know that the area of a rectangle is the product of its length and breadth.
Here the length of the rectangle corresponds to the displacement and the breadth of the rectangle corresponds to the force. Therefore, when we take the area of the rectangle, we are actually calculating the product of force and displacement. The product of force and displacement is the work done by the force. Therefore the area under a curve with force on the Y-axis and displacement on the X-axis will represent the work-done.

Therefore, Option (D): Work-done, is the correct answer.

Note:
A work is said to be done if the point of application of force moves and it is measured by the product of the force and the displacement in the direction of the force. The work done is positive when the point of application of a force moves in the direction of the force.