The boy sledged down a 40 m long mountain in 10 seconds, and then drove along the horizontal

| July 13, 2021 | education

The boy sledged down a 40 m long mountain in 10 seconds, and then drove along the horizontal section for another 20 m to a stop. Find the accelerations in each of the sections and the average speed along the entire path.

V0 = 0 m / s.

S1 = 40 m.

t1 = 10 s.

S2 = 20 m.

V = 0 m / s.

a1 -?

a2 -?

Vav -?

We will assume that in both cases the sleds were moving uniformly, only from the mountain they were accelerated, and in the horizontal section they slowed down.

S1 = V0 * t + a1 * t1 ^ 2/2. Since V0 = 0 m / s, then S1 = a1 * t1 ^ 2/2.

a1 = 2 * S1 / t1 ^ 2.

a1 = 2 * 40 m / (10 s) ^ 2 = 0.8 m / s2.

The speed at the end of the descent V1 is expressed by the formula: V1 = V0 + a1 * t1 = a1 * t1.

V1 = 0.8 m / s2 * 10 s = 8 m / s.

a2 = (V1 ^ 2 – V2) / 2 * S2 = V1 ^ 2/2 * S2.

a2 = (8 m / s) ^ 2/2 * 20 m = 1.6 m / s2.

t2 = (V1 – V) / a ^ 2 = V1 / a2.

t2 = 8 m / s / 1.6 m / s2 = 5 s.

Vav = S / t.

S = S1 + S2.

t = t1 + t2.

Vav = (40 m + 20 m) / (10 s + 5 s) = 4 m / s.

Answer: a1 = 0.8 m / s2, a2 = 1.6 m / s2, Vav = 4 m / s.



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