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