To calculate the average speed of a body traveling from point A to point B with different velocities for each leg of the journey, you need to find the total distance traveled and divide it by the total time taken.
Let's assume the distance from A to B is d.
For the first leg of the journey (A to B), the velocity is 10 m/s. The time taken for this leg is t1 = d / 10.
For the second leg of the journey (B to A), the velocity is 20 m/s. The time taken for this leg is t2 = d / 20.
The total time taken for the entire journey is the sum of the times for each leg: t_total = t1 + t2 = d / 10 + d / 20.
To find the average speed, we divide the total distance (2d, since the body travels from A to B and then back to A) by the total time: average speed = 2d / (t1 + t2) = 2d / (d / 10 + d / 20).
Simplifying the expression, we get: average speed = 2d / (d/10 + d/20) = 2d / (3d/20) = 40d / 3d = 40/3 ≈ 13.33 m/s.
Therefore, the average speed of the body traveling from A to B with a velocity of 10 m/s and from B to A with a velocity of 20 m/s is approximately 13.33 m/s.