3/7 of the way, the body moved at a speed of 50 km / h, and the rest of the way at a speed of 100 km / h.

| August 24, 2021 | education

3/7 of the way, the body moved at a speed of 50 km / h, and the rest of the way at a speed of 100 km / h. Find the average speed.

V1 = 50 km / h.

V2 = 100 km / h.

S1 = 3 * S / 7.

Vav -?

To find the average speed of movement Vav, it is necessary to divide the entire path S passed by the body by the time of its movement t: Vav = S / t.

The travel time of the entire path is expressed by the sum: t = t1 + t2, where t1 is the time of movement on the first section of the path, t2 is the time of movement on the second section of the path.

t1 = S1 / V1 = 3 * S / 7 * V1.

The length of the second track section S2 is S2 = S – S1 = S – 3 * S / 7 = 4 * S / 7.

t2 = S2 / V2 = 4 * S / 7 * V2.

t = 3 * S / 7 * V1 + 4 * S / 7 * V2 = (3 * S * V2 + 4 * S * V1) / 7 * V1 * V2 = S * (3 * V2 + 4 * V1) / 7 * V1 * V2.

Vav = S * 7 * V1 * V2 / S * (3 * V2 + 4 * V1) = 7 * V1 * V2 / (3 * V2 + 4 * V1).

Vav = 7 * 50 km / h * 100 km / h / (3 * 100 km / h + 4 * 50 km / h) = 70 km / h.

Answer: the average body speed was Vav = 70 km / h.



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