Deriving a differential equation for car motion

AI Thread Summary
To derive a differential equation for a car shifting into neutral, it's essential to consider the initial velocity, air drag, and frictional forces. Gravity affects tire traction but is less significant if the tires are rotating freely without braking or acceleration. Friction in the wheel bearings is also a factor but secondary to air drag. Accurately parameterizing air drag will simplify the modeling process. Overall, focusing on these forces will provide a realistic representation of the car's motion.
cytochrome
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I'm looking at this scenario where a car is moving and then shifts into neutral. Knowing the initial velocity, how can I derive a differential equation?

I know the air drag and the frictional force... are there any other forces, like gravity, that should be included to make it realistic? I don't understand what a downward gravitational force would do for this problem
 
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"Downward gravitational force" (weight) would affect the tire traction. But if you are assuming the tires are rotating freely and not dragging on the ground (no braking or acceleration), that should not be an issue. There will, of course, be friction in the wheel bearings.
 
The dominant force is going to be the air drag. That should make things easy for you, if the air drag can be parameterized accurately.

Chet
 

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