How Long Does It Take for a Car to Coast to a Stop?

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SUMMARY

The discussion focuses on deriving the time T it takes for a car to coast to a stop, given the equation of motion a = -C1 - C2v², where C1 and C2 are constants related to the car's mechanical configuration. The aerodynamic resistance is proportional to the square of the car's velocity, while the frictional resistance remains constant. Participants are encouraged to share their attempts and progress in solving this problem, emphasizing the importance of understanding the relationship between velocity and deceleration.

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The aerodynamic resistance to motion of a car is almost proportional to the square of its velocity. Additional frictioal resistance is constant, so that the acceleration of the car when coasting maybe written,
a = - C1 - C2v^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 time T taken for the car to coast to a stop.

Any help is greatly appreciated
 
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Did you attempt at a solution? How far did you get? Where did you stop, and why?
 

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