Find the path S, covered by the train in t = 20 s, if it is known that in the tenth second (n = 10) it has covered the path Sn = 5m.

These tasks: t (considered travel time) = 20 s; S (distance traveled by the train in the tenth second) = 5 m; the initial speed of the train is taken to be zero.
1) Determine the constant acceleration of the train: S (10) = S10 – S9 = a * t10^2 / 2 – a * t9^2 / 2 = a * (0.5t10^2 – 0.5t9^2), whence a = S (10) / (0 , 5t10^2 – 0.5t9^2) = 5 / (0.5 * 10^2 – 0.5 * 9^2) = 0.526 m / s2.
2) Let’s calculate the distance covered in 20 seconds: S = a * t^2 / 2 = 0.526 * 20^2/2 = 105.26 m.
Answer: In 20 seconds, the train covered a distance of 105.26 m.