Final answer:
Using the coefficient of kinetic friction and initial velocity, we calculate the deceleration due to friction, and then use the kinematics equation to determine the time it takes for the car to stop, which is approximately 5.10 seconds.
Step-by-step explanation:
The question pertains to kinetic friction and its role in decelerating a sliding automobile that has locked wheels. We can use the physics concepts of friction and motion to calculate how long it takes for the car to come to a stop.
To find the stopping time, we first need to determine the deceleration caused by kinetic friction. The deceleration a can be calculated using the formula a = μkg, where μk is the coefficient of kinetic friction and g is the acceleration due to gravity. For μk = 0.600 and g = 9.8 m/s2, we have a = 0.600 × 9.8 m/s2 = 5.88 m/s2.
Next, we use the kinematic equation v = u + at to find the stopping time t, where u is the initial speed and v is the final speed (which is 0 m/s since the car stops). Thus, t = (0 - 30.0 m/s) / (-5.88 m/s2) = 5.10 seconds (approximately).
Therefore, it takes approximately 5.10 seconds for the car to come to a complete stop.