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Show that the rate of change of momentum = mass x acceleration. Under what condition does this relation hold?

Answer:

Let force ‘F’ be applied on a body having mass ‘m’ for ‘t’ period of time because of which the velocity of the body changes from u to v.

Hence, the initial velocity of the body is ‘mu’ and final velocity of the body is ’mv’

The difference in the momentum of the body in ‘t’ seconds is given as mv-mu=m(v-u)

Rate of change of momentum = change in momentum/time

= [m(v-u)] /t - equation 1

As we know, acceleration ‘a’=(v-u)/t

Substituting this in the above equation 1, we get;

Rate of change of momentum = mass x acceleration = ma

The condition for this relation to hold true is that mass of the body remains constant.

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