Prove the impulse momentum relation.

The changes in momentum of an object can be connected with
th impulse given to an object.

Let's see
how!

We'll begin with the equation that relates velocity
and force. We know that the force is the result of the product between mass and
acceleration.

F = m*a (1)

The
average acceleration is:

a = dv/dt (2), where v is velocity
and t is time.

We'll write dv = Vt -
V0

and

dt = t -
t0

We'll substitute (2) in
(1):

F = m*dv/dt (3)

F = m*(Vt
- V0)/(t - t0)

Now, we know that to obtain impulse, we need
force and time.

Impulse = F*dt
(4)

We'll substitute (3) in
(4):

Impulse = m*dv*dt/dt

W'll
simplify and we'll get:

Impulse =
m*dv

Impulse = m(Vt -
V0)

We'll remove the
brackets:

Impulse = mVt -
mV0

Impulse = Pt - P0 =
dP