Final answer:
The deceleration of the car can be calculated using the formula deceleration = (final velocity - initial velocity) / time. Given the car's mass, coefficient of kinetic friction, and the fact that it skids to a halt, we can determine the time it takes to decelerate using the formula distance = initial velocity * time + 0.5 * acceleration * time^2.
Step-by-step explanation:
To calculate the deceleration of the car, we can use the formula:
deceleration = (final velocity - initial velocity) / time
Initial velocity = 23 m/s, final velocity = 0 m/s, and time = ? (unknown)
Since the car skids to a halt, we know that the time it takes to decelerate from 23 m/s to 0 m/s is the time it takes to stop. We can find this time using the formula:
distance = initial velocity * time + 0.5 * acceleration * time^2
In this case, the acceleration is the deceleration rate, which is the unknown value we're trying to find. We know the car's mass (2000 kg) and the coefficient of kinetic friction (μk = 0.20).
Using the equation for deceleration, we can solve for time:
deceleration = (0 - 23) / time
-23 = deceleration * time
Since we know the deceleration from the coefficient of kinetic friction (μk = 0.20), we can substitute that value in and solve for time:
-23 = 0.20 * time
time = -23 / 0.20
time = 115 seconds (rounded to the nearest whole number)