Explanation:
The elevator has an acceleration and deceleration of magnitude 1.0 m/s^2, so it takes (5 m/s) / (1 m/s^2) = 5 seconds to reach its maximum speed of 5 m/s.
To come to a stop from this maximum speed, it will also take 5 seconds.
The time it takes for the elevator to travel the entire distance of 200 m is given by:
t = 5 s + 5 s + d / v
where d is the distance traveled at constant speed and v is the constant speed.
We know that the total time is equal to t = 10 s + d / 5 m/s.
Thus, d = (10 s - 5 s) * 5 m/s = 25 m.
So the elevator spends 5 seconds accelerating, 5 seconds decelerating, and 10 - 5 = 5 seconds at constant speed.