First law:A body continues in its state of rest or uniform motion,unless and until an external unbalanced force acts on it.

2nd Law:The second law of motion states that the rate of change of momentum of an object is directly proportional to the applied unbalanced force and it is in the direction of force.

OR

This law states that when a force is applied on a body then the acceleration produced is directly proportional to the applied force and inversely proportional to the mass of the body.



 a is proportional to F/M

=>F is proportional to ma

=>F=K m a

If K=1

=>f=ma

Derivation from momentum:

Suppose an object of mass "m" is moving along with the initial velocity "u".It is uniformly accelerated to velocity "v" in "t" seconds. The initial and the final momentum of the object is  .

The change in momentum is  proportional to

The change in momentum is  proportional to mv-mu

The change in momentum is  proportional to m(v-u)

The rate of change in momentum is proportional to m(v-u)/t

The applied force F is  proportional to m(v-u)/t

=>F=Km(v-u)/t

=>F=Kma

Derivation of first law from the second Law

First law states that A body continues in its state of rest or uniform motion,unless and until an external unbalanced force acts on it.

If F=0

=>ma=0

=>m(v-u)/t=0

=>(v-u)/t=0

=>v-u=0

=>v=u

If u=0 then u=v=0.

Third law of motion:for every action, there is an equal and opposite reaction,the action and the reaction are equal in magnitude but opposite in direction that means they act on different bodies.