The freight train set off with a constant acceleration of 0.5m / s squared, thus reaching a speed of 36km / h. how far he went.

a = 0.5 m / s2.

V0 = 0 m / s.

V = 36 km / h = 10 m / s.

S -?

Since the freight train was moving uniformly accelerated, its traversed path S is determined by the formula: S = V0 * t + a * t ^ 2/2, where V0 is the initial speed of the train, t is the train acceleration time, a is the acceleration during the train acceleration.

Since the train is leaving, its initial speed is V0 = 0 m / s, the formula will take the form: S = a * t ^ 2/2.

We express the acceleration time of the train t from the formula for acceleration: a = (V – V0) / t.

t = (V – V0) / a.

t = V / a.

S = a * V ^ 2/2 * a ^ 2 = V ^ 2/2 * a.

S = (10 m / s) ^ 2/2 * 0.5 m / s2 = 100 m.

Answer: during acceleration, a freight train traveled a distance S = 100 m.