Question

The area under the displacement-force curve gives

• A. Distance traveled
• B. Total force
• C. Momentum
• D. Work done

Answer 1

The correct option is D

Work done

The explanation for the correct option:

In the case of option D,

1. Consider the following displacement-force curve where the $Y$-axis represents the force and the $x$-axis represents the displacement.
2. In the above curve, there is a shaded region which is actually the area under the displacement-force curve. The shape of the shaded region or area is rectangular and we know that the area of the rectangular portion is the product of length and width.
3. Here, the length and width are represented by the displacement and force respectively. So, the area under the displacement-force curve will be as follows.
4. $Area=length\left(displacement\right)\times width\left(force\right)$
5. $Area=workdone$

The explanation for the incorrect options:

In the case of option A,

1. The product of displacement and force represents the work done, not the traveled distance.

In the case of option B,

1. The total force can be defined as the sum of all acting forces.
2. But here in the graph, only one force is acting which is representing the width of the area.

In the case of option C,

1. Velocity can be represented by the area under the acceleration- time graph.
2. But the product of force and displacement can't represent the velocity.

Hence, option D is the correct answer.