Point time has been moving in one direction all this time. Half of the way it moved at a speed

Point time has been moving in one direction all this time. Half of the way it moved at a speed, the modulus of which is 10m / s. And the second half of the way at a speed, the modulus of which is 20 m / s. Determine the average ground speed of the body.

Given:

v1 = 10 m / s – body speed in the first half of the journey;

v2 = 20 m / s – body speed in the second half of the way.

It is required to determine Vav (m / s) – the average speed of the body along the entire path.

Let the entire distance traveled be equal to S. Then, the body passed the first half of the way in time:

t1 = S / (2 * v1).

The body passed the second half of the journey in time:

t2 = S / (2 * v2).

The total travel time is:

t = t1 + t2 = S / (2 * v1) + S / (2 * v2) = S * (v1 + v2) / (2 * v1 * v2).

Then the average speed of movement along the entire path is equal to:

Vav = S / t = S / (S * (v1 + v2) / (2 * v1 * v2)) = 2 * v1 * v2 / (v1 + v2) =

= 2 * 10 * 20 / (10 + 20) = 400/30 = 13.3 m / s.

Answer: The average speed is 13.3 m / s.