Second Law of Motion

Derive the unit of force using the second law of motion. A force of $5 \mathrm{N}$ produces an acceleration of $8 \mathrm{m} {\mathrm{s}}^{-2}$ on a mass $m_1$ and an acceleration of $24 \mathrm{m} {\mathrm{s}}^{-2}$ on a mass $m_2$. What acceleration would the same force provide if both the masses are tied together?

Using second law of motion, derive the relation between force and acceleration. A bullet of $10 \mathrm{g}$ strikes a sand-bag at a speed of ${10}^3 \mathrm{m} {\mathrm{s}}^{-1}$ and gets embedded after travelling $5 \mathrm{cm}$. Calculate the time taken by the bullet to come to rest.