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Show that the rate of change of momentum is equal to product of mass and acceleration.
Let a moving object of mass $m$ is moving with the initial velocity $u$ and a force $F$ is exerted upon it and its velocity becomes $v$ in time $t$ and its acceleration is $a$.
Then, the initial momentum $P_1=mu$
Final momentum $P_2=mv$
Therefore, change in momentum, $\vartriangle P=P_2-P_1=mv-mu=m(v-u)$
So, the rate of the change of momentum in $t$ time $=\frac{\vartriangle P}{t}=\frac{m(v-u)}{t}$
$=ma$ [because acceleration $a=\frac{v-u}{t}$]
$=F$ [as kmnown force $F=ma$]
$=$ applied force
Thus, it has been proved that the rate of change of momentum is equal to the applied force.
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