Question

write Newton's second law of motion and derive F=ma.

Answer 1

Here's ur answer

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 helps:)

Answer 2

Force is change in momentum per unit time.

Or,

Force is directly proportional to (mv - mu)/t

Taking “m” as common.

F directly proportional to {m(v-u)}/t

Now, acceleration = (v-u)/t

Thus,

F directly proportional to m × a

Now we need a constant ‘k’ to convert it into an equation, where k is taken as 1 according tl C.G.S. system.

Hence F = ma

Derivation no. 2:

Force is directly proportional to acceleration.

Or, F directly proportional to ‘a’.

Now, we need a constant ‘k’ to convert this into an equation, where ‘k’ is taken as mass of the moving object om which force is applied.

Hence,

F = m × a

Hope it helped!