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Suppose you apply a constant net
force, F_{net}, to an object of mass
m. Newton's Second Law tells
you that the object will accelerate,
so if it starts with velocity
v_{o}, after some time t its velocity will be v. This
situation is diagrammed below.

The acceleration of the object equals its change in velocity divided by the time it takes the velocity to change. In symbols:

Multiplying both sides of this equation by t gives:

The right side of the equation above comes from the fact that the
change in velocity equals the final velocity, v, minus the starting
velocity, v_{o}. (Note: We could have just as well started
with the kinematics equation v = v_{o} + at.) This is a valid
*kinematical* statement about the motion. To turn it into a*
dynamical* statement about the motion, multiply both sides of the
equation by the object's mass, m:

Since Newton's Second Law tells us that the net force on an object
equals the product of the object's mass and acceleration, we can
replace ma with F_{net} in this equation. On the right side,
the quantity mass times velocity is called momentum, p.

The quantity on the left, F_{net}t, is the impulse exerted
on the object by the net force. The quantity on the right of the
equation is the object's final momentum minus its starting momentum,
which is its change in momentum.

This is the Impulse-Momentum Equation.

Click here for an alternate derivation.

last update January 12, 2010 by JL Stanbrough