The car passed three quarters of its way at a speed of U1 = 40 km / h, the rest of the way at a speed of U2

| March 19, 2021 | education

The car passed three quarters of its way at a speed of U1 = 40 km / h, the rest of the way at a speed of U2 = 72 km / h. What is the average speed (U) of the car?

V1 = 40 km / h.

V2 = 72 km / h.

S1 = 3 * S / 4.

Vav -?

To find the average speed of movement Vav, it is necessary to divide the entire distance traveled by the train S by the time of its movement t along the entire path: Vav = S / t.

S2 = S – S1 = S – 3 * S / 4 = S / 4.

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 = 3 * S / 4 * V1.

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

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

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

Vav = 4 * 40 km / h * 72 km / h / (3 * 72 km / h + 40 km / h) = 45 km / h.

Answer: average vehicle speed Vav = 45 km / h.



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