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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                         As acceleration(a)=(v-u)/t
Δp/t=Force(F)                    As force=m×a 
Hence ,The rate of change of momentum is equal to the force applied.
The rate of change of momentum is directly proportional to the force applied to body.
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Mass of body = m
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. 
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