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# Which law gives a quantitative measurement of the force?

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## Newton's second law of motion:Force is equal to the rate of change of momentum. For a constant mass, force equals mass times acceleration.Suppose an object is moving in a straight line, let $\mathrm{m}$ be the mass of an object moving with initial velocity $\mathrm{u}$ and reachs final velocity of $\mathrm{v}$. If an external force $\mathrm{F}$ is applied for time $\left(\mathrm{t}\right)$ creating an acceleration of $\mathrm{a}$. Then, $\phantom{\rule{0ex}{0ex}}\mathrm{Force}\propto \frac{\mathrm{final}\mathrm{momentum}-\mathrm{initial}\mathrm{momentum}}{\mathrm{time}}\phantom{\rule{0ex}{0ex}}\mathrm{Force}\propto \frac{\mathrm{mv}-\mathrm{mu}}{\mathrm{t}}\phantom{\rule{0ex}{0ex}}\mathrm{Force}\propto \frac{\mathrm{m}\left(\mathrm{v}-\mathrm{u}\right)}{\mathrm{t}}\phantom{\rule{0ex}{0ex}}⇒\mathrm{F}=\mathrm{kma}$ Here, $\mathrm{k}$ is proportionality constant. 3. If 1 unit force is applied on the mass of $1\mathrm{kg}$ and the acceleration created is$1\mathrm{m}/{\mathrm{s}}^{2}$.then,$\mathrm{k}=1$$⇒\mathrm{F}=\mathrm{ma}$Hence, Newton's second law of motion gives a quantitative measure of force.

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