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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Updated on: 10-Oct-2022

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