Question

State Newton's second law of motion and shown that the first law of motion can be mathematically started from the Newton's seconds law.

Answer 1

We know momentum $p=mv$ where m= mass and v=velocity,

So rate of change of momentum $\Delta p=mv-mu$ where v and u are the final and initial velocity.

So rate of change of momentum$=\frac{m(v-u)}{t}$--------(A)

Also we know acceleration $a=\frac{v-u}{t}$

Again Force$F=ma$

Thus A can be written as $F\alpha \frac{m(v-u)}{t}$

$F=kma$ where k= proportionality constant.

Hence from second law of motion we get force is the product of mass and acceleration.

$F=ma$