Question

Or
Derive F =ma from Newton's second law of motion.
-000-​

Answer 1

To ProvE :-

• To Prove that F = ma from Newtons second law of motion .

ProoF :-

The formula of force is ma , where m is mass and a is acceleration .

According to Newton's Second Law :-

• The rate of change of momentum is directly proportional to the applied force in the direction of the force .

• Let us now assume that :-

$\red{\frak{Let}}\begin{cases}\textsf{ Initial velocity be \textbf{u} .}\\\textsf{ Final Velocity be \textbf{v}.}\\\textsf{ Acceleration be \textbf{a} .}\\\textsf{ Time taken to accelerate be \textbf{ t } .}\end{cases}$

Now according to the definition ,

$\sf:\implies \dfrac{\Delta p }{t} \propto F \\\\\sf:\implies F \propto \dfrac{mv - mu }{t}\\\\\sf:\implies F \propto \dfrac{m(v-u)}{t}\\\\\sf:\implies F \propto m\bigg[\dfrac{v-u}{t}\bigg] \\\\\sf:\implies F \propto (m)(a) \\\\\sf:\implies F = kma \qquad\qquad\bigg\lgroup \red{\tt Where \ k \ is \ constant .}\bigg\rgroup \\\\\sf:\implies\orange{\underset{\blue{\sf Hence \ Proved }}{\underbrace{\underline{ \boxed{\pink{\frak{ Force = mass \times acceleration }}}}}}}$