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*For example*, two cars approaching, a canon-bullet system, Passengers in a vehicle. Vehicle may be anything; it may be a bus, a train, a bicycle or anything.

Momentum tells “how much motion the body posses at any instant of time”.

P = M V (P is momentum, M is mass and V is velocity)

If I take the derivative of above equation then I get,

dp/dt = M dv/dt and

dv/dt = acceleration produced in the body.

The term dp/dt tell the variation in momentum w.r.t. time and this is called the derivative of momentum wrt time.

But for the isolated system the total change in momentum is zero.

dp/dt =0 so a = 0

This would mean that either the body is at rest or the body would be moving with uniform velocity.

**Example 1:** A golf ball of mass 50 g at rest is hit by striker if the ball stops at a distance 50m from the origin with uniform retardation of 4 m/s2. Calculate impulse??

**Solution: **By applying the relation v2 - u2 = 2as

Let just after the hitting the velocity of the bullet is u and the final velocity is v which is zero.

a = u2/2s , u = 20 m/s

Impulse = change in momentum = mv - mu = - 1.2 Ns

**Example 2: ** A machine gun has a mass of 20 g. It fires 25 g bullets at the rate of 600 bullets per minute with a speed of 200m/s. Calculate:

1. Recoil velocity of gun

2. Force required to keep the gun in position.

**Solution 1: **Before firing the total momentum is zero for the system, so

0 = m1v1 + m2v2 (where m1, v1 and m2, v2 are the mass and velocity of bullet and cannon respectively.)

So, V2 = -m1v1/m2 (here m1 = 25 g and m2 = 20 kg = 200 m/s)

On substituting values,

V2 = 2.5 m/s

**Solution 2: **Force required to keep the gun in position = total change in momentum of bullets

=d/dt x nmv

(Where ‘ nmv’ represents the total momentum of the bullets)

= 600 x 0.025 x 200/ 60

= 50 N