Final answer:
The time to come to a stop from 60 m/s with an acceleration of -5 m/s² is 12 seconds. The time to reach 40 m/s in the opposite direction is also 12 seconds, totaling 24 seconds to fully reverse direction, which does not match the provided answer choices.
Step-by-step explanation:
To determine how long it takes for a car to reverse direction after initially going at 60 m/s and then starting to go 40 m/s in the opposite direction with an acceleration of -5 m/s², we first need to calculate the time it takes for the car to come to a stop and then the time to reach the speed of 40 m/s in the opposite direction.
The car initially decelerates from 60 m/s to 0 m/s with an acceleration of -5 m/s². The formula to calculate the time (t) is t = (v_f - v_i) / a, where v_f is the final velocity, v_i is the initial velocity, and a is the acceleration.
Using the formula: t = (0 m/s - 60 m/s) / -5 m/s² = 12 seconds. This is the time it takes to come to a stop.
Next, we need to calculate how long it takes to reach 40 m/s in the opposite direction, but since the acceleration remains the same and the desired change in velocity is the same magnitude, it will also take 12 seconds. Therefore, the total time to completely reverse direction is 12 seconds + 12 seconds = 24 seconds. However, this is not an answer option, indicating a potential error in the question setup or provided answer choices.