The first quarter of the way, the car travels at a speed of 40 km / h, and the rest of the way is 40 km / h.

| August 2, 2021 | education

The first quarter of the way, the car travels at a speed of 40 km / h, and the rest of the way is 40 km / h. Find the average vehicle speed.

V1 = 40 km / h.

V2 = 60 km / h.

S1 = S / 4.

Vav -?

To find the average vehicle speed Vav, it is necessary to divide the entire path S it has traveled by the time of its passage: 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 / 4 * V1.

Since the first part of the path S1 is S1 = S / 4, then the second part of the path is S2 = S – S1 = S – S / 4 = 3 * S / 4.

t2 = S2 / V2 = 3 * S / 4 * V2.

t = S / 4 * V1 + 3 * S / 4 * V2 = (S * V2 + 3 * S * V1) / 4 * V1 * V2 = S * (V2 + 3 * V1) / 4 * V1 * V2.

Vav = S * 4 * V1 * V2 / S * (V2 + 3 * V1) = 4 * V1 * V2 / (V2 + 3 * V1).

Vav = 4 * 40 km / h * 60 km / h / (60 km / h + 3 * 40 km / h) = 53.3 km / h.

Answer: the average vehicle speed is Vav = 53.3 km / h.



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