Traveling at a speed of 18.5 m/s, the driver of an automobile suddenly locks the wheels by slamming on the brakes. The coefficient of kinetic friction between the tires and the road is 0.690. What is the speed of the automobile after 1.41 s have elapsed? Ignore the effects of air resistance.

-m g (.69) = m a

a = - .69 g

v = 18.5 - .69(9.8)(1.41)

Thank you

To find the speed of the automobile after 1.41 seconds have elapsed, we can use the equation of motion:

vf = vi + at

Where:
vf = final velocity
vi = initial velocity
a = acceleration
t = time

We know that the initial velocity (vi) is 18.5 m/s and the time (t) is 1.41 s. To find the acceleration (a), we need to calculate the net force acting on the automobile.

The net force can be determined using the equation:

F_net = μ * F_normal

Where:
F_net = net force
μ = coefficient of kinetic friction
F_normal = normal force

To find the normal force (F_normal), we need to consider the gravitational force acting on the automobile, which is equal to its weight (W). The weight can be calculated using the equation:

W = m * g

Where:
m = mass of the automobile
g = acceleration due to gravity (typically 9.8 m/s^2)

First, calculate the weight of the automobile. Let's assume the mass is 1000 kg:

W = 1000 kg * 9.8 m/s^2
W = 9800 N

Next, find the normal force (F_normal) by considering that it is equal in magnitude and opposite in direction to the gravitational force. Therefore:

F_normal = -9800 N

Now, calculate the net force (F_net) by multiplying the coefficient of kinetic friction (0.690) by the normal force:

F_net = 0.690 * (-9800 N)
F_net = -6762 N

Since the force of friction opposes motion, it is negative.

Now, we can find the acceleration (a) using Newton's second law of motion:

F_net = m * a

Rearranging the equation, we have:

a = F_net / m

Assuming a mass of 1000 kg:

a = -6762 N / 1000 kg
a = -6.762 m/s^2

Now that we have the acceleration, we can substitute the values into the equation of motion:

vf = vi + at

vf = 18.5 m/s + (-6.762 m/s^2) * 1.41 s
vf = 18.5 m/s - 9.559 m/s
vf = 8.941 m/s

Therefore, the speed of the automobile after 1.41 seconds have elapsed is approximately 8.941 m/s.