State the relation between the momentum of a body and the force acting on it.

Relation between the momentum of a body and the force acting on it:

The rate of the change of the momentum of a body with respect to time is equal to the force acting on it. 

If a body of mass $m$ is moving with the initial velocity $v_1$ and after acting a force $F$ on it, and its velocity becomes $v_2$ in within a time period $t$,

Then, change in momentum $=P_2-P_1=mv_2-mv_1$

Therefore, rate of change of momentum $=\frac{m(v_2-v_1)}{t}$

$=m(\frac{v_2-v_1}{t})$

$=ma$      [because rate of change of velocity is acceleration, $a=\frac{v_2-v_1}{t}$]

$=F$       [According to Newton's second law of motion $F=ma$]

$=$ Force acted on the body

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Updated on: 10-Oct-2022

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