Solving Friction Problem - Accelerating Car Without Spilling Coffee

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Please help...
A person places a cup of coffee on the roof of her car while she dashes back into the house for a forgotten item. When she returns to the car, she hops in and takes off with the coffee cup still on the roof.
(a) If the coefficient of static friction between the coffee cup and the roof of the car is 0.24, what is the maximum acceleration the car can have without causing the cup to slide? Ignore the effects of air resistance.


(b) What is the smallest amount of time in which the person can accelerate the car from rest to 20 m/s and still keep the coffee cup on the roof?

so I don't really even know where to start. How would I know what mu is?
 
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How would I know what mu is?

It's given in the question.

What is the equation for the frictional force?

By the way, this is not advanced physics. This should be in the introductory physics forum (for future reference). :smile:
 
How much does the cup weigh?

Dont you need its mass?
 
No, you don't need the mass. It will cancel out in the end.
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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