An object with mass 162 kg is given an initial downward velocity $\displaystyle -{2}\frac{{m}}{{s}}$ in a medium that exerts a resistive force with magnitude proportional to the square of the speed. The resistance is 80 N when the velocity is $\displaystyle -{2}\frac{{m}}{{s}}$. Use $\displaystyle {g}={10}\frac{{m}}{{{s}^{{2}}}}$

a. Write out a differential equation in terms of the velocity $\displaystyle {v}$, and acceleration $\displaystyle {a}$

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b. Find the velocity $\displaystyle {v}{\left({t}\right)}$ for the object

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c. Upload a document with the work for parts a and b and a computer generated graph of the solution.

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d. State and interpret the end behavior for the solution found in part b.