Question

Derive Formula from the statement " Rate of change of momentum is directly proportional to force "

Answer 1

Hey there!

Given rate of change of momentum is directly proportional to its Force applied.

First of all

Momentum =P = mv

Rate of change of velocity = Pf - Pi /t

Here Pi is the initial momentum,

Pf is the final momentum


now

Pf - Pi /t ∝F

mv- mu /t ∝ F

we know that final and initial velocities are considered v,u respectively.

m( v - u)/t ∝F

F ∝ ma

here we take acceleration = v-u/t

So for removing proportionality I am introducing a proportionality constant Say K

finally F= maK

here K =1

Finally F = m* a

Force is the product of the mass of the object and acceleration produced.

hope helped!

Answer 2

hii dear friend


formula

mometntum is to directly proportional

ACCORDING TO Newton 2nd law

lets see

initial momentum of the body = MU

final momentum of the body = mv

cheng in momentum = mu - mv

lets see

= mu-mv/ t

= M (V- U ) /t

= Ma [ Q a = v-u/t ]

..............

And direct to force

F= Ma or Fa = k ma


its depend on unit..