The boy rides on a sled with uniform acceleration from a snow slide. The speed of the sled

The boy rides on a sled with uniform acceleration from a snow slide. The speed of the sled at the end of the descent is 10 m / s. acceleration is 1m / s ^ 2, initial speed is 0. Find the length of the slide.

V0 = 0 m / s.

V = 10 m / s.

a = 1 m / s2.

S -?

The path S traversed by the sled is expressed by the formula: S = V0 * t + a * t2 / 2, where V0 is the initial speed of movement, a is the acceleration of movement, t is the time of descent from the hill.

Since the initial speed of the sled is V0 = 0 m / s, the formula will take the form: S = a * t2 / 2

We express the time t of the sled descending from the hill from the formula for acceleration: a = (V – V0) / t, where V is the speed of the sled at the end of the descent.

t = (V – V0) / a.

Since V0 = 0 m / s, then t = V / a.

t = 10 m / s / 1 m / s2 = 10 s.

S = 1 m / s2 * (10 s) 2/2 = 50 m.

The length of the slide can also be expressed by the formula: S = (V2 – V02) / 2 * a.

S = V2 / 2 * a.

S = (10 m / s) 2/2 * 1 m / s2 = 50 m.

Answer: the slide has a length of S = 50 m.