Question

deduce newtons first law from second law(9......)

Answer 1

Newton’s Second Law of Motion states that the rate of change of momentum of a body is directly proportional to the force applied on the body and the change in momentum is in the direction of the force applied.

Mathematically,

F⃗ =mΔp⃗ F→=mΔp→

Where p⃗ p→ is the momentum vector.

Per unit time,

F⃗ =ma⃗ .F→=ma→.

Now, Newton’s First Law states that A body at rest continues to be in a state of rest and a body in motion continues to be in a state of uniform motion until and unless an external, unbalanced force acts on the body, which changes its state of rest or uniform motion.

Here, we are dealing with a case of uniform motion OR rest. Both of these cases are very special because there is one thing common — the velocity of the body is constant. Hence, the acceleration of the body over time is 0 (This is important).

Let us take the mathematical expression for the Second Law — this time without vectors (for simplicity).

F=maF=ma

But, if the body is in uniform motion, acceleration is 0. Hence

Answer 2

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.