Question

The area under force time curve represents
(A) Work
(B) Momentum
(C) Power
(D) Impulse

Answer 1

Hint: Power is the amount of energy transferred or converted per unit time. In other words, power is the rate of doing work. We need to use Newton’s second law of motion to derive the relation between Force and time. We shall be taking a special case of constant mass in this case.

Complete Step by Step Solution:
Newton's second law of motion states that the rate of change of momentum of a body over time is directly proportional to the force applied, and occurs in the same direction as the applied force.
Mathematically, force $ F = \dfrac{{dp}}{{dt}} $ where $ p $ is momentum and $ t $ is time.
For objects and systems with constant mass, the second law can be stated in terms of an object's acceleration.
 $ F = m\dfrac{{dv}}{{dt}} $
Rearranging the equation, we can write, $ Fdt = mdv $ .
Integrating the equation on both the side,
 $ F\int {dt} = m\int {dv} $
 $ \Rightarrow F \cdot t = mv $
This product of the force and time is called impulse.
Thus, we can say that impulse is the integral of a force, over the time interval, for which it acts. Since force is a vector quantity, impulse is also a vector quantity. Impulse applied to an object produces an equivalent vector change in its linear momentum, also in the same direction.
The area under force time curve represents Impulse.
Hence, the correct answer is Option D.

Note:
We shall define the other parameters provided in the options.
Work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, it is often represented as the product of force and displacement.
Momentum refers to the quantity of motion that an object has. As discussed earlier, force is the rate of change of momentum.