Question

prove that rate of change of momentum is equal to force​

Answer 1

Answer:

initial velocity =mu

final velocity= mv

change in velocity = mv-mu

=m(v-u)

the rate of change of momentum =m(v-u) /t

we know that force= mass x acceleration

a=v-u/t

force = m(v-u) /t

hence proved

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