Prove that the average speed of a bus moving from point A to point B at a speed v1, and from

| September 4, 2021 | education

Prove that the average speed of a bus moving from point A to point B at a speed v1, and from B to A at a speed v2, is less than or equal to (v1 + v2) / 2

Let L be the distance between points A and B. Then the average speed of the bus for a full trip from point A to point B and back is equal to:

vav = L full / t full = 2 * L / (L / v1 + L / v2) = 2 * L / (L * (v1 + v2) / v1 * v2) =

= 2 * L * v1 * v2 / (S * (v1 + v2) = 2 * v1 * v2 / (v1 + v2).

In this case, Ltot is the distance that the bus travels back and forth, ttotal is the time it takes for the bus to leave point A and return to the same point.

Now we divide the resulting equation for the average speed with the equation for comparison:

2 * v1 * v2 / (v1 + v2) / (v1 + v2) / 2 = 4 * v1 * v2 / (v1 + v2) ^ 2 =

= 4 * v1 * v2 / (v1 ^ 2 + 2 * v1 * v2 + v2 ^ 2) – the resulting equation will always be less than or equal to one, which means that the average speed will always be less than or equal to the value (v1 + v2) / 2 …



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.