Question

Is the impulse-momentum relationship related to Newton's second law?

Answer 1

Hint: Before we proceed into the problem, it is important to know about the newton’s second law and impulse-momentum relationship. We can write the mathematical expression of both relations to determine whether they are related or not.
Newton’s second law of motion relates mass of the body and its acceleration.On the other hand impulse-momentum relates mass of the body and velocity gradient.

Complete answer:
Newton’s Second Law of Motion states that the rate of change of linear momentum of a body is directly proportional to the force applied on the body, and this change takes place always in the direction of the force applied. The equation is given by
$F = m\vec a$
Where,
m = mass of body
a = acceleration of body
The impulse-momentum theorem states that the rate of change of momentum of a body is equal to the impulse applied to it. The formula is given as follows:
$J = F\Delta t = m\Delta v$
Where,
$\Delta v = $change in velocity of an object

From Newton's Second Law, you know that to accelerate a body, a net force must be applied to it. The impulse-momentum relationship is basically the same thing, but expressed differently. It says that if you wish to change the momentum of an object, you need to exert an impulse on it.

Note: These two equations seem different in a mathematical sense but have the same meaning as acceleration is rate of change of velocity per unit time. Impulse-momentum has an expression of velocity gradient which is similar to acceleration. Also impulse-momentum is used when dealing with fluid.