# 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 2^{nd} 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 2^{nd} 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.

Hey it’s too good i clearly understood the law

its to good we can easily get 3 marks in examination

it would be clearer if u mentioned p=mv and v/t=a and thus ma arises out,

anyways good work and thanks.

From F=ma, if we derive for acceleration it is, a=F/m…As per this the unit of acceleration would become Newton/Kilogram (N/kg)…

But the actual unit of acceleration is m/s^2…

I am confused…

A Newton is a kgm/s^2. So a kgm/s^2/kg leaves a unit of m/s^2. You just have to break the Newton down into its components to cancel the kg and get the acceleration in typical units.

I have been lurking though the textbook and guides to understand the derivation !

This finally helped me ! Thanks a lot

I cannot understood it properly…….

What is the meaning of-dp & dt??!!!

easy steps

Take care when you equate Newtonian linear distance d and the circumferential distance which is pi x d (diameter). This holds on knowing that Einstein’s energy is radiated energy and hence involves circular geometry. Otherwise you cannot derive Einstein’s infamous energy formula from Newton’s second law of motion!!!