Final answer:
The final velocity of the car is found to be -6.11 m/s after decelerating from an initial speed of 13.89 m/s with a constant deceleration of 0.400 m/s² for 50 seconds. This result is unreasonable because a high coefficient of friction would not allow the car to continue moving in the opposite direction after stopping. The premise that the car continues to decelerate at the same rate without stopping is unreasonable.
Step-by-step explanation:
The question asks about the final velocity of a car that decelerates from an initial speed of 50.0 km/h with a constant deceleration of 0.400 m/s² for a duration of 50.0 seconds. To find the final velocity, we will first convert the initial velocity from km/h to m/s by using the conversion factor (1 km/h = 1/3.6 m/s).
Initial velocity, vi = 50.0 km/h = 50/3.6 m/s ≈ 13.89 m/s.
Using the kinematic equation, vf = vi + at, where vf is the final velocity, vi is the initial velocity, a is acceleration, and t is time:
vf = 13.89 m/s - (0.400 m/s² × 50.0 s) = 13.89 m/s - 20 m/s = -6.11 m/s.
The negative value indicates that the car would have come to a stop and then reversed direction. However, with a high coefficient of friction of 1.0, it is unreasonable to expect that the car would continue to move in the opposite direction after stopping, as the frictional force should bring it to a halt much sooner.
The unreasonable premise is the assumption that the car can decelerate at a constant rate over the time period without the influence of friction bringing it to a stop before reversing direction.