The first half of the journey the car drove at a speed of 50 km / h; the second half of the journey

| February 25, 2021 | education

The first half of the journey the car drove at a speed of 50 km / h; the second half of the journey, the car drove at a speed of 60 km / h. What is the average speed of the vehicle for the entire driving time?

V1 = 50 km / h.

V2 = 60 km / h.

S1 = S2 = S / 2.

Vav -?

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

The travel time of the entire path is expressed by the sum: t = t1 + t2, where t1 is the travel time on the first half of the path, t2 is the time of movement on the second half of the path.

With uniform rectilinear movement, time is determined by the ratio: 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 * 50 km / h * 60 km / h / (60 km / h + 50 km / h) = 54.5 km / h.

Answer: the average speed of the vehicle was Vav = 54.5 km / h.



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