Figure $1\mathrm{.}33$ A speedboat decelerating by virtue of drag.

Combining the hydrodynamic force with Newton's second law of motion yields $\frac{dv}{dt}=-k_1{v}^2,$

where $k_1=\frac{k}{M}.$ For this boat $k_1=0\mathrm{.}025m^{-1}.$

a$.$ What is the boat initial velocity, $v(0)?$

b$.$ Find the boat velocity $v(t).$

c$.$ Find the boat distance $x(t)$ using $x(0)=0$ as the IC when the engines shut off.