by newtons 2nd law of motion,
momentum is directly proportional to F
hence dp/dt proportional to F
F=k(dp/dt)
in si unit k=1
F=dp/dt=d(mv)/dt
since m is const.
Hence F=ma
Or
Let us derive the relation of force F = ma from Newton’s second law:
According to the Newton’s 2nd Law of motion, the rate of change of linear momentum of a body is directly proportional to the applied external force and in the direction of force.
It means that the linear momentum will change faster when a bigger force is applied.
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.