Question

Derive the relation between force apply acceleration produce using in netwon second law of motion​

Answer 1

According to second law of motion
F=change in momentum per unit time
F=∆p/∆t…………………(1)

As we know p=mv
So change in momentum (∆p)=∆(mv)
∆p=m∆v.................... (2)
(since mass is constant and only velocity changes)

Also acceleration a=change in velocity per unit time
a=∆v/∆t…………………(3)

Using (1)&(2)
F=m∆v/∆t
Using (3)
F=ma

This is the relation between force and acceleration which you are looking for

Answer 2

Here is your answer.

Newton 2nd law of motion.

Formula, Force = m × a

F = ma

where F is net force , m is mass , a is acceleration.

If a force produces an acceleration @ in a body of mass then we state matimatically that,

a is proportional to F.

and

a is inversely proportional to mass = 1÷ mass

or

a is proportional to F ÷ m

change the places of terms.

F is proportional to ma

Putting k as proportionality constant we get,

equal instead of proportional sign F = kma

in SI units value of K comes out to be 1.

So F = 1 ( ma)

F = ma

and SI unit of force is Newton ( N ).

hope you understand it ...