Question

state and prove newton's second law of motion

Answer 1

Explanation:

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.

Answer 2

Answer:

Newton's Second Law of Motion states that the acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, is in the same direction as the net force, and is inversely proportional to the mass of the body.

ᴩʀᴏᴠᴇ

So,

F = $\large\rm\frac{dP}{dt}$

But P = mv

So, F = $\large\rm\frac{d(mv)}{dt}$

F = $\large\rm m×\frac{dv}{dt}$

⟹ F = ma