The car moves uphill at a speed of 20 m / s, and on a descent 25 m / s. Find the average speed if the ascent length is 4 times the length of the descent.
Vp = 20 m / s.
Vs = 25 m / s.
Sп = 4 * Sс.
To find the average vehicle speed Vav, it is necessary to divide the entire path S it has traveled by the time of its movement t: Vav = S / t.
The travel time of the entire path is expressed by the sum: t = tp + tc, where tp is the time of movement on the rise, tc is the time of movement on the descent.
tп = Sп / Vп = 4 * Sс / Vп.
tс = Sс / Vс.
t = 4 * Sc / Vp + Sc / Vc = (4 * Sc * Vc + Sc * Vp) / Vp * Vc = Sc * (4 * Vc + Vp) / Vp * Vc.
The entire path S traveled will be the sum: S = Sп + Sс = 4 * Sс + Sс = 5 * Sс.
Vcr = 5 * Sc * Vp * Vc / Sc * (4 * Vc + Vp) = 5 * Vp * Vc / (4 * Vc + Vp).
Vav = 5 * 20 m / s * 25 m / s / (4 * 25 m / s + 20 m / s) = 20.8 m / s.
Answer: the average vehicle speed was Vav = 20.8 m / s.
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