Question

Derive from newton second law of motion the first law of motion.

Answer 1

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.

Answer 2

from 2nd law,
F= ma
=> F= m× (v-u/ t)
for a body moving with constant velocity, v= u
therefore, F= m×0= 0
thus, no force is required to move a body with constant velocity. For a body which is at rest.
u=0=v
therefore, the body will remain at rest if no external force is applied on a body and hence, 1st law is derived