The motorcycle traveled the first half of the path at a speed of 15 m / s and the second at a speed of 30

| August 9, 2021 | education

The motorcycle traveled the first half of the path at a speed of 15 m / s and the second at a speed of 30 m / s, determine the average speed of the motorcycle.

V1 = 15 m / s.

V2 = 30 m / s.

S1 = S2 = S / 2.

Vav -?

To find the average speed of the motorcyclist Vav, it is necessary to divide the entire path S traveled by him by the time of his 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 half of the path, t2 is the time of movement on the second half of the path.

t1 = S1 / V1 = S / 2 * V1.

t2 = S2 / V2 = S / 2 * V2.

t = S / 2 * V1 + S / 2 * V2 = (S * V2 + S * V1) / 2 * V1 * V2 = S * (V2 + V1) / 2 * V1 * V2.

Vav = S * 2 * V1 * V2 / S * (V2 + V1) = 2 * V1 * V2 / (V2 + V1).

Vav = 2 * 15 m / s * 30 m / s / (30 m / s + 15 m / s) = 20 m / s.

Answer: the average speed of a motorcyclist was Vav = 20 m / s.



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