Question

using 2 law of motion drive relation b/w force and accleration

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.

Answer 2

Consider a body of mass ‘m’ moving with velocity v.

The linear momentum of a body is given by:

p = mv

Now According to Newton’s 2nd Law of Motion:

Force is directly proportional to rate of change of momnetum, that is

F α dp/dt

F  = k dp/dt

F = k d(mv)/dt

F = k md(v)/dt

F = k ma

Experimentally k =1

F = k ma

Which is the required equation of force.