The cyclist traveled the first half of the journey at a speed of V1 = 12 km / h and the second half of the journey

| April 19, 2021 | education

The cyclist traveled the first half of the journey at a speed of V1 = 12 km / h and the second half of the journey at a speed of V2. What is the speed of V2 if the average speed along the entire path is 8 km / h

V1 = 12 km / h.

S1 = S2 = S / 2.

Vav = 8 km / h.

V2 -?

The average speed of movement Vav is determined by the formula: Vav = S / t, where S is the entire path traveled by the cyclist, t is the time of movement along the entire path.

The time of movement along the entire path t is found by the formula: 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 * (V1 + V2) / 2 * V1 * V2.

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

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

Vav * V1 + Vav * V2 = 2 * V1 * V2.

V2 = Vav * V1 / (2 * V1 – Vav).

V2 = 8 km / h * 12 km / h / (2 * 12 km / h – 8 km / h) = 6 km / h.

Answer: V2 = 6 km / h.



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