Derive relation F = ma from Newton 2nd Law of Motion

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.


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