Explain the impulse-momentum theorem. Please explain the physics. So far to expl

Question

Explain the impulse-momentum theorem. Please explain the physics.

So far to explain the impluse momentum theorem and physics involved I have written:

Impulse is the rate of change of momentum or the product of net force acting on an object and it's duration. Momentum is the quantity that describes an objects resistance to stopping, and is the product of velocity and mass. The impulse-momentum therorem states that since impulse is equal to change in momentum, and momentum is equal to the product of mass and velocity, that the product of mass and velcocity is equal to the net force acting on an object over a duration of time.

That's as far as I got, I am stuck as to where the equation Fdt = mdv + vdm fits and how to interpret that equation into words ( I do not understand what this eqaution means really, need it explained in words), and i am also confused as how this relates to newtons second law, and how to put that realtionship into words. Thanks for your help in advance.

PLEASE DO NOT JUST GIVE ME EQUATIONS. This will not help me and I will give you a thumbs down. I am looking for words to explain the realtionship with newtons second law, and what that equation above means. PLEASE explain to me like I am stupid because I am.

Explanation / Answer

I've put text in italics and in [] for your better understanding. Omit them suitably if you are coplying it to somewhere.

Impulse is the change of momentum [not the rate of change] of an object when an external force is applied on it, both in magnitude and in direction because both, force and velocity are vector quantities. Hence, Impulse is the product of net force acting on an object and the duration for which the force acts.

Momentum is a parameter associated with a body in motion [that which describes an object’s resistance to change in constant motion or rest/stopping is inertia]. Momentum is the product of velocity and mass at a particular instant.   

p          = m x v

For momentums at two instances, we can denote them as p1 and p2 at two time instances t1 and t2. Force F is applied from t1 to t2 which changes the velocity of the body from v1 to v2.

Hence we have        p1        = m x v1                     initial momentum

and p2        = m x v2                     final momentum

The impulse-momentum theorem states that impulse is equal to change in momentum,

Which means           J           = p2 – p1 (final - initial)

                                              = m x v2 - m x v1

                                                = m x ( v2 – v1)                                 … (1)

As per the second law, force applied is equal to mass of body times the rate of change of velocity,

Or,                              F         = m x dv/dt

If you multiply both sides by dt [in principle, not mathematically], you will get-

                                    F dt     = m x dv   + v x dm

Here, we are not considering a body of changing mass [because that’s not actually possible unless its travelling near the speed of light and it gets really sentimental]

So, change in mass, dm = 0

And                             F dt     = m x dv                                                         … (2)

By observing (1) and (2) above, we can say that

                                                J = F dt

Or impulse is the [constant] external force applied on an object for a duration t2 - t1 [i.e. dt]

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