Hello students now we are going to proceed towards the next law, i.e. second law of motion proposed by Sir Isaac Newton. This law relates the force and momentum of body. We know that momentum is defined as the product of mass and velocity of body. Hence, P= mv. SI unit of momentum is kg.m/s

When there is change in momentum of body, force associated with it also changes, which was predicted by Sir Newton and stated in his 2^{nd} law as ‘rate of change of momentum is directly proportional to the impressed force, and the change in momentum is takes towards the direction of applied force.’

This law is very important in understanding the mathematical form of force with which we can find the magnitude of force acting on the body.

To learn 2^{nd} law, consider the following illustration,

Suppose the bullet of mass ‘m’ is thrown on wall with velocity of v_{1}, so that the initial momentum of bullet can be,

P_{1}= mv_{1}.

Now imagine that after time ‘t’ the same bullet is fired with help of gun on the same wall with velocity of v_{2}, then its momentum will be

P_{2}= mv_{2}.

Now we can easily predict that the impact on wall in 2^{nd} case will be higher than that of 1^{st} case, then change in momentum can be

∆P = P_{2} – P_{1}

∆P = mv_{2} – mv_{1}

∆P = m(v_{2 }-v_{1})………………….(1)

According to second law of motion, we can have,

As the mathematical form for force was given by Newton, hence the SI unit of force is named after him, i.e. netwon (N)

Equation (2) and (3) are the mathematical forms of Newton’s second law of motion.

**Ex: A bullet of mass 200 g, accelerates with 50 m/s ^{2} on wooden plank, what is the magnitude of force acts on plank?**

**Solution:**

m= 200 g= 0.2 kg

a=50 m/s^{2}

According to second law of motion, we can have,

F = m a = 0.2 × 50 = 10 N

**Ex: What should be acceleration of car of mass 2000 kg which exerts force of 10000 N when collides on a tree?**

**Solution: ** m= 2000 kg

F= 10000 N

According to second law of motion, we can have,

F=m a

a= F/m = 10000/2000 = 10/2 = 5 m/s2