Question

State Newton's second law of motion and derive it mathematically?

Answer 1

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 $p_{i} , p_{f}$ 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

Newton Second law of motion=''According to
the rate of change of momentum is directly proportional to applied force and takes place in the same direction as the applied force''.

$\infty sign \: of \: proportinality$
MATHMATICAL EXPRESSION OF NEWTONS 2 LAW OF MOTION =
F= Force
M= Mass
U= Initial Velocity
V= Final Velocity
T= Time
P= Momentum
Initial Momentum = MU
Final Momentum = MV
Change in Momentum = MV-MU
= M(V-U)
$rate \: of \: chnge \: of \: momentum = \frac{m(v - u)} {t}$
$we \: know \: that \: \frac{( v - u)}{t} = a$
Now Put,
Rate of change of Momentum
Now, F proptional to MA
F= KMA (K= constant)
the value of K is 1
Then, (F=MA)

HOPE THIS HELPS...