The driver of the car changed the speed every minute, the driver of the motorcycle changed the speed every kilometer.

| August 5, 2021 | education

The driver of the car changed the speed every minute, the driver of the motorcycle changed the speed every kilometer. Who has a higher average speed if the speeds are respectively equal to 40 km / h, 60 km / h, 80 km / h, 20 km / h

V1 = 80 km / h.

V2 = 20 km / h.

S1 = S2 = 1 km.

V3 = 40 km / h.

V4 = 60 km / h.

t3 = t4 = 1 min = 1/60 h.

Vav -?

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 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 = S1 / V1.

t2 = S2 / V2 = S2 / V2 = S1 / V2.

t = S1 / V1 + S1 / V2 = (S1 * V2 + S1 * V1) / V1 * V2 = S1 * (V2 + V1) / V1 * V2.

S = S1 + S2 = 2 * S1.

Vav = 2 * S1 * V1 * V2 / S1 * (V2 + V1) = 2 * V1 * V2 / (V2 + V1).

Vav = 2 * 80 km / h * 20 km / h / (20 km / h + 80 km / h) = 32 km / h.

S = S3 + S4.

S3 = V3 * t3 = V3 / 60.

S4 = V4 * t4 = V4 / 60.

S = V3 / 60 + V4 / 60 = (V3 + V4) / 60.

t = t1 + t2 = 1/60 + 1/60 = 1/30.

Vav “= (V3 + V4) * 30/60 = (V3 + V4) / 2.

Vav “= (40 km / h + 60 km / h) / 2 = 50 km / h.

Answer: the average speed of the motorcyclist was Vav = 32 km / h, the average speed of the vehicle was Vav “= 50 km / h.



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