Impulse

Impulse is defined as the change in momentum of an object, also in kg m/s. By the impulse-momentum change theorem, the impulse is defined as:

Now, proving this is very easy but let's prove it assuming the net force is constant with respect to time, allowing us to use the approximation at the end of the image above. If we assume that, here's how we get to this equation.

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First, let's remember net force as a change in momentum(impulse) over the change in time. If we take mass to be constant, it's the product of mass and the change in velocity over change in time. If we cross-multiply change in time to force's side, we get that the product of force and change in time is the same as the product of mass and change in velocity. Mathematically, this is:

Now, with calculus, this is pretty much the same thing except you use "dt" and not delta t. Remember, that this gives you the change in momentum, not the total momentum. As you do when integrating functions, to know the actual value of an object's momentum, you need to know its initial momentum plus its change in momentum to know its momentum at any given point.