Traveling at a speed of 18.0 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 1.29 s have elapsed? Ignore the effects of air resistance.

To find the speed of the automobile after 1.29 seconds have elapsed, we can use the equation of motion:

v = u + at

where:
v = final velocity
u = initial velocity
a = acceleration
t = time

Since the driver slams on the brakes, the acceleration is in the opposite direction of motion. The acceleration can be calculated using the equation:

a = -μ * g

where:
μ = coefficient of kinetic friction
g = acceleration due to gravity (approximately 9.8 m/s^2)

In this case, the initial velocity is 18.0 m/s, the coefficient of kinetic friction is 0.690, and the time is 1.29 seconds.

First, calculate the value of acceleration:

a = -0.690 * 9.8
a = -6.762 m/s^2

Next, substitute the values into the first equation of motion:

v = 18.0 + (-6.762) * 1.29
v = 18.0 - 8.71998
v = 9.28002 m/s

Therefore, the speed of the automobile after 1.29 seconds have elapsed is approximately 9.28 m/s.

To find the final speed of the automobile after 1.29 seconds with locked wheels, we can use the equation for acceleration due to friction:

a = μ * g

Where "a" is the acceleration, μ is the coefficient of kinetic friction, and g is the acceleration due to gravity (approximately 9.8 m/s²).

Given that the coefficient of kinetic friction is 0.690, we can calculate the acceleration:

a = 0.690 * 9.8 = 6.762 m/s²

Since the automobile is slowing down due to the acceleration, the equation to find the final speed is:

v = u + a * t

Where "v" is the final speed, "u" is the initial speed (18.0 m/s), "a" is the acceleration, and "t" is the time elapsed (1.29 seconds).

Substituting the values into the equation:

v = 18.0 m/s + (6.762 m/s²) * (1.29 s)

Calculating:

v = 18.0 m/s + 8.720 m/s

v = 26.720 m/s

Therefore, the speed of the automobile after 1.29 seconds have elapsed is approximately 26.720 m/s.

F = - .69 m g = m a

so
a = -.69 g

v=Vi + a t
v = 18.0 - .69 g t
v = 18 - .69(9.81)(1.29)