Question

state newton's second law of motion.show that force is the product of mass and acceleration

​

Answer 1

${\bold{\blue{\underline{\red{An}\pink{sw}\green{er}\purple{:-}}}}}$

➤Newton's second law of motion:-

☛ According to Newton's second law of motion,the rate of change of linear momentum of a body with respect to time is directly proportional to the unbalanced force applied on the body and change in momentum take place in the direction of appiled force.

∴ $\pink{\underline{\boxed{\bf{Force\propto\:\dfrac{Change\:in\:momentum}{Time\:taken}}}}}$

$\rm\:{p_i}=mu$

$\rm\:{p_f}=mv$

$\rm\Delta{p}={p_f}-{p_i}$

$\rm\Delta{p}=mv-mu$

Now,

$\rm\:f\propto\:\dfrac{\Delta{p}}{\Delta{t}}$

$\rm\:f\propto\:\dfrac{mv-mu}{t}$

$\rm\:f\propto\:\dfrac{m(v-u)}{t}$

$\rm\:f\propto\:ma$

$\rm\:f=kma$

$\rm\:k=1$

$\red{\underline{\boxed{\bf{F=ma}}}}$