Final answer:
The maximum acceleration a car can undergo given a coefficient of static friction of 0.80 is approximately 7.848 m/s^2. This is calculated using the relationship between static friction force, coefficient of static friction, the normal force, and the car's mass.
Step-by-step explanation:
Maximum Acceleration and Coefficient of Static Friction
To calculate the maximum acceleration a car can undergo given a coefficient of static friction (μs) of 0.80, we can use the fundamental physics of friction and motion. In the absence of an incline, the maximum acceleration a car can achieve without slipping is a function of the static friction force and the mass of the car. The static friction force (Fs) is the product of the coefficient of static friction and the normal force (N), which, on flat ground without any incline, is equal to the weight of the car (W = m * g, where m is the mass of the car and g is the acceleration due to gravity). The formula to calculate the static friction force is:
Fs = μs * N
Since Fs is also equal to the mass of the car times its acceleration (Fs = m * a), we can set these two equations equal to each other and solve for the acceleration (a). This gives us: a = μs * g
By substituting the given coefficient of static friction (0.80) and the acceleration due to gravity (approximately 9.81 m/s2), we can calculate the maximum acceleration:
a = 0.80 * 9.81 m/s 2 = 7.848 m/s 2
Therefore, the maximum acceleration of the car without slipping, given a coefficient of static friction of 0.80, is approximately 7.848 m/s2.