Question

State the Newton's second law of motion and deduce F=ma

Answer 1

hello frnd,
here ur answer,

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.

hope this answer will clear ur doubts,
mark it brainliest,
best wishes

 

Answer 2

Newton's Second law of motion :- The rate of change of momentum is directly proportional to the force applied on the system. 

Force applied is directly proportional to the product of mass and acceleration .

Let  be the initial and final momentums respectively.

According to newton's second law :- 

pf - pi / t ∝ F 

We know that, Momentum ( P) = mv .

Let v be the final and u be the initial velocity .

Now, 

mv - mu / t ∝ F 

F ∝ m ( v-u) /t

F ∝ ma. 

F = kma. 

Here, K is the proportionality constant. It's value is 1 .

Units of Force are given by the units of mass and acceleration. Units of force is Kgm/s² .

In accordance to honour the contributions of Newton, 1 kgm/s² is termed as 1 Newton

Hope it's helpful mate