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Since the coefficient of kinetic friction does not depend on velocity, and therefore the frictional force does not, then why does a car barely accelerate when the tires are spinning quickly like when someone is doing a burnout?

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  • $\begingroup$ Because the driver applies the brakes during a burnout. Otherwise you have a rolling burnout which does accelerate the car. $\endgroup$ – ja72 Mar 22 '18 at 21:26
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If the coefficient of kinetic friction is constant, why does a car barely accelerate while its tires are spinning?

It's due to the coefficient of kinetic friction being much lower than the coefficient of static friction. In the case of a tire that is rolling without slipping, the tire's contact patch with the ground has zero velocity with respect to the ground. This means static friction is in play. A torque applied to the tires means the car accelerates nicely, at least so long as the torque isn't so high as to make the tire start slipping.

It's game over with regard to that nice acceleration if the tires do start to slip. Now the contact patch is moving with respect to the ground, so the lower coefficient of kinetic friction rules. This coefficient is much lower than is the limiting value for static friction. The car still accelerates, but not nicely.

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