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Change in momentum(Δp)=Δ(mv)

mass will only change when the speed of this particular mass is near the speed of light So,

for c being very very large than the v

Δp=mΔv or m(v-u)

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

Δp/t=m×a

The rate of change of momentum is directly proportional to the force applied to body.

initial velocity = u

final velocity = v

time taken = t

change in momentum (Δp) = pf-pi

= mv -mu

rate of change of momentum = (mv-mu)/t

⇒ F α (mv-mu)/t

⇒ F α [m(v-u)]/t

⇒ F α ma

⇒ F = kma

Here k = proportionality constant.