Question

State Newton’s second law of motion. Derive F = ma​

Answer 1

Answer

Derive the expression F=ma. Hint: According to Newton's second law of motion the force is equal to the rate of momentum. The change in momentum which is also known as impulse is the product of the mass and the velocity. ... Hence the unit of force is Newton or kgm2.

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Answer 2

Explanation:

Newton’s second law of motion states that the force exerted by a body is directly proportional to the rate of change of its momentum. For a body of mass ‘m’, whose velocity changes from u to v in time t, when force ‘F’ is applied.

$\underline{{F}\mathrm{\propto}\frac{{Change}\hspace{0.33em}{in}\hspace{0.33em}{momentum}}{Time}}$

$\underline{{F}\mathrm{\propto}\frac{{mv}\mathrm{{-}}{mu}}{t}}$

$\underline{{F}\mathrm{\propto}{m}{\mathrm{(}}\frac{{v}\mathrm{{-}}{u}}{t}{\mathrm{)}}}$

$\underline{\mathrm{\Rightarrow}{F}\mathrm{\propto}{ma}\mathrm{\Rightarrow}{Kma}\left({{a}\mathrm{{=}}\frac{{v}\mathrm{{-}}{u}}{t}}\right)}$

$\underline{\mathrm{\Rightarrow}{F}\mathrm{{=}}{ma}{\mathrm{(}}{k}\mathrm{{=}}{cons}\tan{t}\mathrm{{=}}{1}{\mathrm{)}}}$

Hence proved

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