Question

derive mathematical expression of second law of motion ​

Answer 1

Answer:

#See solution for details.

Explanation:

Newton's Second law of motion states that :- the rate of change of momentum is directly proportional to the force applied on an object or system..

The force applied on an object of mass m is directly proportional to the product of mass and acceleration:

$F=ma$

-Let $p_1$ be the initial momentum and $p_2$ be the final momentum.

$p_2-\frac{p_1}{t}\propto F$

#also let $u$ be the initial velocity and $v$ the final.

Momentum,$P$:

$P=mv$

$mv-\frac{mu}{t}\propto F\\\\F\propto \frac{m(v-u)}{t}\\\\F\propto ma\\\\F=kma$

#where k is the constant of proportionality. Given the direct proportion, k=1.

#The unit is in kgm/s but usually equated to N, 1kgm/s=1N