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

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In summary, the aerodynamic resistance and additional frictional resistance of a car affect its motion. The acceleration of a coasting car can be expressed as a function of velocity, with constants C1 and C2 depending on the car's mechanical configuration. To determine the time for the car to stop, an expression can be derived using the initial velocity and the acceleration equation.
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superman.
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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?
 

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

What factors affect the time taken for a car to stop?

The time taken for a car to stop can be affected by several factors including the speed of the car, the condition of the brakes, the weight of the car, and the road conditions.

How does the speed of the car impact the time taken to stop?

The higher the speed of the car, the longer it will take to come to a complete stop. This is because the car has more momentum and takes longer to slow down.

What role do brakes play in the time taken to stop?

The condition of the brakes is crucial in determining the time taken for a car to stop. Worn out or faulty brakes will take longer to bring the car to a stop, increasing the overall stopping distance.

Does the weight of the car affect the time taken to stop?

Yes, the weight of the car has a significant impact on the time taken to stop. Heavier cars have more momentum and require more force to stop, making the stopping distance longer.

How do road conditions influence the time taken for a car to stop?

The road conditions, such as wet or icy surfaces, can have a significant impact on the time taken for a car to stop. These conditions decrease the level of friction between the tires and the road, making it harder for the car to stop quickly.

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