State Newton’s second law of motion and show that the first law of motion can be mathematically started from Newton’s second’s law

Answer: Newton’s second law of motion states that the rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of force.

To Show: Mathematical Derivation of Newton’s first law of motion from the second law of motion.

According to the second law of motion,

F = m*a 

Or F = m (v -u)/t (As acceleration = v-u/t, where u = initial velocity and v = final velocity)

Or Ft = mv – mu

It implies that for any given time t, v = u in case F = 0. And hence the object will maintain a constant velocity u while moving throughout the time duration t. Even when u = 0, it would imply that v = 0 and the object will continue to remain in the state of rest.