Linear momentum is a measure of an object's translational motion. The linear momentum p of an object is defined as the product of the object's mass m times its velocity v.
p = mv.
Linear momentum is a vector. Its direction is the direction of the velocity. The Cartesian components of p are
px = mvx, py = mvy, pz = mvz.
If an object's velocity is changing, its linear momentum is changing. We have
dp/dt = d(mv)/dt.
If the mass of the object is constant then
dp/dt = mdv/dt = ma.
dp/dt = F.
This is a more general statement of Newton's second law which also holds for objects whose mass is not constant.
If an object receives an impulse, its momentum changes. We may write
dp = Fdt.
If the force acting on the object is constant, then
∆p = F∆t.
The integral of force over time is called the impulse I of the force. We have shown that the impulse I is equal to the change in momentum ∆p. You give an object an impulse, by letting a force act on it for a time interval ∆t.
I = ∆p = Favg∆t
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