A 346 kg car is accelerating down an asphalt road. Between asphalt and rubber, the coeficient of static friction is 1.23 and the coefient of kinetic friction is .98 What is the fastest the car can accelerate?

If the tires apply a force against the road of less than or equal to 1.23w (where w is the weight of the car, i.e. the force normal to the roadway), the wheels maintain their traction, and the car experiences an equal and opposite force which accelerates it down the road. If the wheels try to exceed that force, they will slip, and then the maximum possible frictional force is reduced to 0.98w. So clearly the maximum achievable force is 1.23w.

So what's the value of w? It's the force from gravity, w=mg.

Thus you have .

Once you know the force applied to the car, you can easily calculate its acceleration from Newton's 2nd law, F=ma.

Note that even though you were told the mass of the car, ultimately you don't even need that information. The mass will end up dividing out, and the maximum acceleration is only a function of the coefficient of friction and the acceleration of gravity.