The train passes the first 10 km at a speed of 30 km, the second 10 km / h at 40 km / h

| February 1, 2021 | education

The train passes the first 10 km at a speed of 30 km, the second 10 km / h at 40 km / h, the third 10 km at a speed of 60 km / h, what is the average speed along the entire route?

S1 = 10 km.

V1 = 30 km / h.

S2 = 10 km

V2 = 40 km / h.

S3 = 10 km.

V3 = 60 km / h.

Vav -?

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

The travel time of the entire path is expressed by the sum: t = t1 + t2 + t3, where t1 is the time of movement of the first part of the path, t2 is the time of movement on the second part of the path, t3 is the time of movement on the third part of the path.

Since S1 = S2 = S3, then S = 3 * S1.

With uniform rectilinear motion, the motion time t is expressed by the formulas: t1 = S1 / V1, t2 = S2 / V2, t3 = S3 / V3.

t = S1 / V1 + S2 / V2 + S3 / V3 = (S1 * V2 * V3 + S2 * V1 * V3 + S3 * V1 * V2) / V1 * V2 * V3 = S1 * (V2 * V3 + V1 * V3 + V1 * V2) / V1 * V2 * V3.

Vav = 3 * S1 * V1 * V2 * V3 / S1 * (V2 * V3 + V1 * V3 + V1 * V2) = 3 * V1 * V2 * V3 / (V2 * V3 + V1 * V3 + V1 * V2).

Vav = 3 * 30 km / h * 40 km / h * 60 km / h / (40 km / h * 60 km / h + 30 km / h * 60 km / h + 30 km / h * 40 km / h) = 40 km / h.

Answer: the average train speed is Vav = 40 km / h.



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