# Derive newtons first law of motion from second law.

Newton's second law states that F=ma.
Assuming that no external force is being applied on the body, i.e., F=0,
0 = ma
=> 0 = m [(v-u)/t]
=> 0/m = (v-u)/t
=> 0*t = v-u
​=> 0 = v-u
=> u = v
According to Newton's first law of motion, a body moving with a certain velocity continues to move with the same velocity, i.e., u=v; until and unless an external force is applied, which may change the speed of the body.
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2nd law
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According to Newton's 2nd law F=mv-mu/t fxt=mv-mu If F=0(no external force) 0xt=mv-mu 0=mv-mu mu=mv m and m cancelled on both the sides u=v or v=u (constant velocity) If u=0(body is at rest). v=u=0 v=u
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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.
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