Impulse Momentum Theorem (constant and variable motion)?

Momentum…

is a quantity that describes an object's resistance to stopping (a kind of "moving inertia").
is represented by the symbol p (boldface).
is the product of an object's mass and velocity.

p=mv

is a vector quantity (since velocity is a vector and mass is a scalar).

Impulse…

is a quantity that describes the effect of a net force acting on an object (a kind of "moving force").
is represented by the symbol J (boldface).
is the product of the average net force acting on an object and its duration.

J=F̅Δt

is the force–time integral.

J= ⌠
⌡ Fdt

is a vector quantity (since force is a vector and time is a scalar).

Impulse-Momentum Theorem

The impulse-momentum theorem states that the change in momentum of an object equals the impulse applied to it.

J=Δp

If mass is constant, then…

F̅Δt=mΔv

If mass is changing, then…

Fdt=mdv+vdm

The impulse-momentum theorem is logically equivalent to Newton's second law of motion (the force law).

Units

The SI unit of impulse is the newton second.
The SI unit of momentum is the kilogram meter per second.
These units of impulse and momentum are equivalent.