Question

prove that the rate of change in linear momentum is equal to force​

Answer 1

Answer:

Theorem: The rate of change of the total momentum of a system of particles is equal to the sum of the external forces on the system. But, by Newton's third law of motion, Fji+Fij=0, so the theorem is proved. ... (Law of Conservation of Linear Momentum.)

hope this is helpful for you.

Answer 2

Answer:

$\maltese\underline{\textsf{\textbf{AnsWer :}}}\:\maltese✠$

Let initial momentum ($p_i$) be mu

Let final momentum ($p_f$) be mv

According to 2nd law of motion

$\frac{p_f - p_i}{t} \propto \: f$

$\implies \: f \propto \frac{mv \: - mu}{t}$

$\implies \: f \propto \frac{m(v - u)}{t}$

$f \propto \: ma \: \: \: \: \: \: ( \frac{v - u}{t } = a )$

To remove the proportionality sign. We would add k as the proportionality constant

$f = kma \\ f = ma \:$

because by the definition of force k = 1