The cyclist covered the first half of the journey at a speed of 18 km / h. Determine its speed on the second

| September 23, 2021 | education

The cyclist covered the first half of the journey at a speed of 18 km / h. Determine its speed on the second half of the journey, if the average speed along the entire path is 12 km / h?

V1 = 18 km / h.

Vav = 12 km / h.

S1 = S2 = S / 2.

V2 -?

To find the average speed of movement Vav it is necessary. the entire path of movement S is divided by the time of its passage t: Vav = S / t.

The entire traversed path S will consist of the sum: S = S1 + S2.

The travel time of the entire path t will be the sum: t = t1 + t2.

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

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

t1 + t12 = S / 2 * V1 + S / 2 * V2 = S * (V1 + V2) / 2 * V1 * V2.

Vav = S / (t1 + t2) = 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.

Vav * V1 = 2 * V1 * V2 – Vav * V2.

V2 = Vav * V1 / (2 * V1 – Vav).

V2 = 12 km / h * 18 km / h / (2 * 18 km / h – 12 km / h) = 9 km / h.

Answer: the speed of the cyclist on the second half of the journey was V2 = 9 km / h.



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