Understanding Braking Distance: Weight & Slide to Stop Time

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When braking, the weight of the car does not affect the "slide to stop" time because both inertia and deceleration forces are proportional to the car's mass. The inertia is represented by the formula ma, while the deceleration force is calculated as mgk, where g is gravity and k is the coefficient of friction. When these two forces are equated, the mass cancels out, leading to a constant deceleration rate. This means that the deceleration is solely determined by the coefficient of friction and gravity, not the car's weight. Understanding this principle clarifies why weight does not influence stopping time under the specified conditions.
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I haven't taken physics in my college curriculum yet, so could someone help me understand why when slamming the brakes on my car, the weight of my car isn't a factor in the "slide to stop" time? Assuming I am not pulling weight behind me (trailor or something) and I have no collision with anything inbetween slamming on the brakes and stopping. Thanks!
 
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The reason is that the both the inertia and the deceleration force are proportional to the car's mass. The first is ma, and the second is weight times coefficient of friction k, or mgk. Equate the two and the mass cancels. Deceleration a is equal to gk. C'est tout.
 
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