Question

derive newton first and third law by second law

Answer 1

Consider an isolated system of 2 bodies A & B. An isolated system means where there is no external force acting.Now let F be the force acting on B by A & F be the force acting on A by B.Now rate of change of momentum of A =dpA/dt and rate of change of momentum of B =dpB/dt

thus FAB=dpB/dt (i)......

FBA=dpA/dt (ii)........

Adding 1 and 2 we get FAB+FBA=dpB/dt+dpA/dt =d(pB+pA)/dt

But if no force is applied momentum will also be 0 because no velocity will be there so rate of change of momentum will also be 0

thus d(pA+pB)/dt=0

therefore FAB+FBA=0

or,FAB=-FBA

(3RD LAW OF MOTION)

Answer 2

For a constant mass m,

Newton's second law looks like:

F = m * (V1 - V0) / (t1 - t0)

The change in velocity divided by the change in time is the definition of the acceleration a.

The second law then reduces to the more familiar product of a mass and an acceleration:

F = m * a.

thanks for that,