a$)$ An object is thrown into a fluid with an initial velocity of $50\frac{m}{s}.$ In the fluid, the object experiences a drag force leading to an acceleration represented by the empirical formula $a=g-0\mathrm{.}02v^{2\mathrm{.}5}\frac{m}{s^2}$ where $g=9\mathrm{.}81\frac{m}{s^2}.$ Determine the time it takes for the velocity to be reduced to $20\frac{m}{s}$ and the distance it traveled during that time.

Hint: Apply the differential relations $a=d\frac{v}{d}t$ and ads$=vdv$ and then use integral formulation. Use MATLAB built$-$in function integral to complete the solution.

b$)$ Using the acceleration equation from problem $4$a$,$ plot the distance traveled as a function of the velocity from $50\frac{m}{s}$ to $20\frac{m}{s}.$