Question

Derive newton 1st law and 3rd law of motion from newtons 2nd law of motion ...???

Answer 1

NEWTON'S FIRST LAWThe body moves (accelerates) when a force is applied to it that is
F = ma --> a = F / m
When there is no force acting onthe body (F = 0), then the body won't move or would remain in motion with constant velocity (won't accelerate in both cases: a = 0), why? Because
a = F / m and F =0 --> a = 0
So we can state the first law: A body will remain at rest or constant velocity unless a force in acted upon it.



NEWTON'S SECOND LAW
According to the Newton’s 2nd Law of motion, the rate of change of linear momentum of abody 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.

Answer 2

1st Law states that an object will continue without a change in motion constant velocity if there are no outside forces

2nd Law states that to have an acceleration, there must be an outside force.
∑F=m⋅a

If F = 0

∑F=m⋅a becomes 
0=m⋅a
0=a

And if there is no acceleration, there is no change in motion 1st law