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 − C₂v², 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.

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Problem 2/43