You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.
system
<image>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>
A. $D=\frac{1}{C_{2}}\ln(1+\frac{C_{2}}{C_{1}}v_{0}^{2})$
B. $D=\frac{1}{2C_{2}}\ln(1+\frac{C_{1}}{C_{2}}v_{0}^{2})$
C. $D=\frac{1}{2C_{2}}\ln(1+\frac{C_{2}}{C_{1}}v_{0}^{2})$

Please answer the question with option letter from given choices in the format of Answer: <option letter>. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
user
C
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>
A. $D=\frac{1}{C_{2}}\ln(1+\frac{C_{2}}{C_{1}}v_{0}^{2})$
B. $D=\frac{1}{2C_{2}}\ln(1+\frac{C_{1}}{C_{2}}v_{0}^{2})$
C. $D=\frac{1}{2C_{2}}\ln(1+\frac{C_{2}}{C_{1}}v_{0}^{2})$

Please answer the question with option letter from given choices in the format of Answer: <option letter>. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
val