The aerodynamic resistance to motion of a car is nearly proportional to the square of its velocity. Additional frictional resistance is constant, so that the acceleration of the car when coasting may be written a = -C1 - C2*v^2, where C1 and C2 are constants which depend on the mechanical configuration of the car. If the car has an initial velocity v0 when the engine is disengaged, derive an expression for the distance D required for the car to coast to a stop.<image 1>
['$D=\\frac{1}{C_{2}}\\ln(1+\\frac{C_{2}}{C_{1}}v_{0}^{2})$', '$D=\\frac{1}{2C_{2}}\\ln(1+\\frac{C_{1}}{C_{2}}v_{0}^{2})$', '$D=\\frac{1}{2C_{2}}\\ln(1+\\frac{C_{2}}{C_{1}}v_{0}^{2})$']