The athlete, having run a hundred meters, began to stop at the moment of crossing the finish line

The athlete, having run a hundred meters, began to stop at the moment of crossing the finish line and completely stopped at a distance of 10 meters behind it. Determine how long it took the athlete to run the distance if his maximum speed was 11 m / s (during acceleration and deceleration, the speed varied evenly)

1) To determine how long it took an athlete to run the distance, if his maximum speed was Vo = 11 m / s and, having run a hundred meters, he began to stop at the moment of crossing the finish line and completely stopped only at a distance of S = 10 meters behind it, we find braking time first.
The distance traveled by the athlete during braking (V = 0m / s) can be expressed by the formula for calculating the path with equal slow motion of the body: S = (V + Vо) • t: (2) or S = (Vо) • t: (2) … Determine the braking time from this formula: t = 2S: Vо. Let us substitute the values ​​of physical quantities from the condition of the problem and make calculations: t = 2 • 10 m: (11 m / s); t = 1.818 s.
2) The acceleration time on the path S = 100 m is found in the same way, taking into account that during acceleration and deceleration, the speed varied uniformly: t = 2 • 100 m: (11 m / s); t = 18.182 s. In total, the athlete ran: 1.818 s + 18.182 s = 20 s.
Answer: the athlete ran for 20 seconds, of which he ran the 100-meter distance in 18.182 seconds.