# Prove the impulse momentum relation.

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### 1 Answer

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**