For two thirds of the entire time, the body moved at a speed of 10 m / s, for the remaining time

univerkov | August 7, 2021 | education

For two thirds of the entire time, the body moved at a speed of 10 m / s, for the remaining time, half of the way at a speed of 2 m / s, and the rest of the way at a speed of 30 m / s. Find the average speed along the way.

Vav. = S / t, where S = S1 + S2 + S3, t = t1 + t2 + t3.

1) t1 = 2/3 t, where V1 = 10 m / s; S1 = V1 * t1.

t2,3 = t – t1 = t – 2/3 t = 1/3 t.

2) V2 = 2 m / s; t2 = S2 * V2.

3) V3 = 30 m / s; t2 = S3 * V3.

S2 = S3 = V2 * t2 = V3 * t3 = 2 * t2 = 30 * t3; t2 = 15t3; t2 + t3 = 16t3 = 1/3 t and t3 = 1/48 t.

Vav. = (V1 * 2/3 t + V2 * t2 + V3 * t3) / t = (10 * 2/3 t + 2 * t2 + 30 * t3) / t = (10 * 2/3 t + 2 * 15t3 + 30 * t3) / t = (10 * 2/3 t + 60t3) / t = (10 * 2/3 t + 60 * (1/48 t)) / t = 20/3 + 60/48 = 7 , 92 m / s.

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