An object with mass $37\mathrm{.}5$ kg has an initial downward velocity of $-27\frac{(m)}{(s)}.$ Assume that the atmosphere exerts a resistive force with magnitude proportional to the speed. The resistance is $-45$ N when the velocity is $-3\frac{m}{s}.$ Use $g=10\frac{(m)}{s^2}$

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

$37\mathrm{.}5a=-375-15v$

b$.$ Find the velocity $v(t)$ for the object

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c$.$ Upload a document with the work for parts a and b and a solution curve.

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d$.$ Interpret the solution by describing what happends to the object. Include the initial conditions and end behavior for the solution found in part b in your explanation.